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  • Mathematics and Statistics
  • Wiley-Blackwell  (76)
  • Annual Reviews
  • 2005-2009
  • 1990-1994  (76)
  • 1980-1984
  • 1991  (76)
  • 1
    Electronic Resource
    Electronic Resource
    On mathematical modelling of absorption and dispersion of seismic waves for low frequencies (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 563-572 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero.General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann-Hilbert problems for analytic functions in the upper half-plane.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/mma.1670140804
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  • 2
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    Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 525-552 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑m and their complementary parts ∑m′ are prescribed. Making use of the Fourier transform a representation formula for H1 (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener-Hopf (WH) system for jumps of the Dirichlet-and Neumann-Cauchy data across the semi-infinite screens ∑m. The (2N × 2N)-Fourier symbol matrix SP contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑m.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670140802
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  • 3
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    Convergence analysis for a multiplicatively relaxed EM algorithm (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 573-593 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The expectation maximization (EM) algorithm is an iterative procedure used to determine maximum likelihood estimators in situations of incomplete data. In the case of independent Poisson variables it converges to a solution of a problem of the form min ∑[〈ai,x〉 - bi log 〈ai, x〉] such that x ≥0. Thus, it can be used to solve systems of the form Ax = b, x≥0 (with A stochastic and b positive.) It converges to a feasible solution if it exists and to an approximate one otherwise (the one that minimizes d (b, Ax), where d is the Kullback-Leibler information divergence). We study the convergence of the multiplicatively relaxed version proposed by Tanaka for use in positron emission tomography. We prove global convergence in the underrelaxed and unrelaxed cases. In the overrelaxed case we present a local convergence theorem together with two partial global results: the sequence generated by the algorithm is bounded and, if it converges, its limit point is a solution of the aforementioned problem.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670140805
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  • 4
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    The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 35-61 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of a unique, global classical solution of the quantum Vlasov-Poisson problem posed on the phase space ∝x3 × ∝v3. The proof is based on a reformulation of the quantum Vlasov-Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger-Poisson problem is first analysed on a bounded domain in ∝x3 and the solution of the whole-space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ∝x3.
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    URL: http://dx.doi.org/10.1002/mma.1670140103
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  • 5
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    Dynamical shape control and the stabilization of non-linear thin rods (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 63-78 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well-posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress-strain relation is both non-linear and non monotone, so that hysteresis effects arising from solid-solid phase transitions in the rod are included.
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    URL: http://dx.doi.org/10.1002/mma.1670140104
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  • 6
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140301
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  • 7
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    Entropy compactification in Lagrangean gas dynamics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 207-216 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140305
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  • 8
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    An approximation of the thermal field in a continuous casting process of a thin metal layer (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 217-226 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670140402
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  • 9
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140501
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  • 10
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    The problem of equivalence in statistical mechanics of equilibrium (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 319-331 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace-Stieltjes transform of the so-called microcanonical partition function equal to a Legendre transform of the logarithm of the latter? The conditions we shall formulate turn out to be physically reasonable.
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    URL: http://dx.doi.org/10.1002/mma.1670140504
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  • 11
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    Charge transport in semiconductors with degeneracy effects (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 301-318 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi-Dirac distribution into the classical drift-diffusion model. In this work a Boltzmann equation with a non-linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.
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    URL: http://dx.doi.org/10.1002/mma.1670140503
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  • 12
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    Asymptotic completeness in optical scattering (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 333-354 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper time-dependent methods are developed in order to prove the existence of the wave operators and asymptotic completeness in the scattering theory of electromagnetic waves in inhomogeneous media.The medium has a localized perturbation of the dielectric susceptibility. There are no regularity assumptions about the dielectric susceptibility.It is shown directly that the range of the wave operator is the complete continuous subspace, and not just the absolutely continuous subspace of the generator of the time evolution describing the perturbed wave propagation.
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    URL: http://dx.doi.org/10.1002/mma.1670140505
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  • 13
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    On the linear piezoelectricity of composite materials (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 403-412 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: From the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.
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    URL: http://dx.doi.org/10.1002/mma.1670140604
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  • 14
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    An integral operator related to the stokes system in exterior domains (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 445-445 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140608
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  • 15
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140801
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  • 16
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    Generalized limiting absorption method and multidimensional inverse scattering theory (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 509-524 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We generalize the classical limiting absorption method. This generalization is applied to the study of the Faddeev-Lippmann-Schwinger equations in the Faddeev-Newton approach to multidimensional inverse scattering theory. In particular, we give a new proof, under more general conditions than were known previously, of the absence of exceptional points for small potentials and large values of the parameters, and on the existence of real exceptional points if there are complex ones, in particular for potentials that produce negative eigenvalues.
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    URL: http://dx.doi.org/10.1002/mma.1670140705
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  • 17
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    The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 595-613 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the global existence of a unique classical solution of the two-dimensional Wigner-Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.
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    URL: http://dx.doi.org/10.1002/mma.1670140902
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  • 18
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140101
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  • 19
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140201
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  • 20
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    The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 93-119 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density ρ of the fluid and is identically equal to zero for ρ ∊ 〈0, ρ2〉 (where, ρ2 is a given positive number). If ρ2 is chosen sufficiently large, the system coincides with the Navier-Stokes equations and the equations of continuity if the density has values that actually appear in real flows. The velocity is assumed to be equal to zero on the boundary of the flow field and the body force is not taken into account. Initial conditions need not be ‘small enough’. Applying the method of discretization in time, the existence of a weak solution on an interval of an arbitarary (but finite) length is proved and an estimate of the energy character is derived.
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    URL: http://dx.doi.org/10.1002/mma.1670140203
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  • 21
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    A half-space problem for a non-linear Boltzmann equation arising in semiconductor statistics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 121-137 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In semiconductors the distributions of electrons satisfy a non-linear Boltzmann-Vlasov equation. We consider the half-space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering distribution. We establish that this solution tends towards a Fermi-Dirac distribution exponentially fast.
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    URL: http://dx.doi.org/10.1002/mma.1670140204
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  • 22
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    An artificial boundary condition for an advection-diffusion equation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 155-175 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the advection-diffusion equation: u1 + aux1 - vδu = 0 in ∝n × ∝+ with initial data u0; the Support of u0 is contained in ∝-n(x1 〈 0) and a: ∝n → ∝ is positive. In order to approximate the full space solution by the solution of a problem in ∝-n × ∝+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v.
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    URL: http://dx.doi.org/10.1002/mma.1670140302
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  • 23
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    Non-linear flexings in a periodically forced floating beam (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 1-33 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free-end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non-linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small- and large-amplitude solutions can exist. Numerical evidence is presented, which shows that the large-amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp-like surface for the multiple solutions.
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    URL: http://dx.doi.org/10.1002/mma.1670140102
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  • 24
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    Boundary value problems to a certain class of non-linear diffusion equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 79-92 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The first initial-boundary value problem and the free boundary of Stefan's type for a certain class of non-linear diffusion equations which arises in plasma physics are considered. For the first initial-boundary value problem, the global existence of a classical and its large-time behaviour are discussed. The free-boundary problem is studied by the reduction to the first initial-boundary value problem.
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    URL: http://dx.doi.org/10.1002/mma.1670140202
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    Global existence of weak solutions for a system of non-linear Boltzmann equations in semiconductor physics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 139-153 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L2-estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.
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    The blow-up rate for the heat equation with a non-linear boundary condition (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 197-205 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 27
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    On the mildly degenerate Kirchhoff string (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 177-195 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let us consider the Cauchy problem for the abstract evolution equation, which describes the Kirchhoff sring u″ + m(〈Au, u〉) Au = 0, (t 〉 0), Where ( )′ = d/dt, A is any symmetric isomorphism of a Hilbert space V into its (anti) dual V′ and m is a function of one real variable. Following physical considerations, we allow m(·) to be any non-decreasing, non-negative continuous function (a degenerate Kirchhoff string).We assume that the initial value u0 satisfies: m(〈Au0, u0〉)〉0 (a mildly degenerate Kirchhoff string), that m is locally Lipschitz continuous in the open region where it does not vanish, and that m has a finite order of vanishing (e.g., m(ρ) = ργ, γ 〉 0).We establish the local well-posedness of the Cauchy problem in the class D(Aα/2) × D(A(α-1)/2), For each α ≥ 3/2. This improves the results of Medeiros and Miranda [15], Ebihara et al.[9] and a result of Yamada [27].We are not able to prove the global existence of the solution; however, we provide a lower estimate for the life span of the solution, which yields the almost global existence (AGE) in the case when m(ρ) = ργ (γ〉0).
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    URL: http://dx.doi.org/10.1002/mma.1670140303
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    Optimal control of thermomechanical phase transitions in shape memory alloys: Necessary conditions of optimality (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 265-280 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The necessary conditions for the optimality of an optimal control problem associated with soiid-solid phase transitions in shape memory alloys are established.
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    URL: http://dx.doi.org/10.1002/mma.1670140404
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    A uniqueness theorem in the dynamical theory of piezoelectricity (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 295-299 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution to the linearized equations of dynamical linear piezoelectricity is shown to be unique without requiring definiteness conditions in the elastic coefficients. Only continuity of the normal component of the electric displacement field across the boundary between the elastic body and free space is required. The proof employs a logarithmic convexity argument.
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140601
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    Diffraction by an acoustically transmissive or an electromagnetically dielectric half-plane (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 387-402 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half-plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half-plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half-plane. The asymmetry of the approximate boundary condition results in a matrix Wiener-Hopf problem, which is solved explicitly.
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    Global smooth solution for a coupled non-linear wave equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 419-425 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, the global existence and uniqueness of smooth solution to the initial-value problem for coupled non-linear wave equations are studied using the method of a priori estimates.
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    Solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $$\end{document}. Exact solutions of some partial differential equations in mechanics and physics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 615-631 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $\end{document}, for L̂ a linear operator are derived. Different forms for L̂ whether it is time independent or time dependent and self-commutative (or not) at different times are considered separately. By using the results obtained, exact solutions of some partial differential equations are found for the first time.
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    Masthead (1991)
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    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Resonances in periodic media (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 227-263 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear acoustic waves (a) in an infinite string with a periodic material distribution, (b) in an infinite cylinder with a meterial distribution that is periodic in the longitudinal direction and does not depend on the transverse coordinates. We assume that the wave field is generated by a time-harmonic force distribution of frequency ω acting in a compact set. We show in both cases that resonances of order t1/2 occur for a discrete set of frequencies and that the solution is bounded as t→∞ for the remaining frequencies. In case (a) ω is a resonance frequency if and only if ω2 is a boundary point of one of the spectral bands of the corresponding spatial differential operator of Hill's type. A similar characterization of the resonance frequencies is given in case (b).
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    Differential stability of solutions to parametric optimization problems (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 281-294 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A method for the differential stability of solutions to a class of solutions to a class of parametric optimization problem is prposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space H2(Ω)onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second-order elliptic equation are derived.
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    On the theory of cylindrical resonators (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 355-375 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper contains an introduction to the methods of operator-valued functions for solving some non-linear eigenvalue problems of the electrodynamics of guided waves. One simple example of the problem of fundamental frequencies for the rectangular-slot resonator is considered that gives an opportunity to follow all the steps and features of this technique.
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    On a class of ill-posed non-linear integral equations arising in the interpretation of indirect measurements (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 377-386 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we consider a class of specific Urysohn integral equations for which the solutions are only determined with the exception of rearrangements of function values and associated arguments. As an alternative to Tikhonov's regularization method approximating minimum-norm solutions for this ill-posed class of inverse problems, a constrained least-squares approach is presented. This approach is aimed at finding decreasing rearrangements serving as appropriate solution representatives. It is shown that the inverses of these decresing solutions solve a Fredholm linear integral equation of the first kind.
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    Blow-up for semilinear parabolic equations with a gradient term (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 413-417 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 447-460 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.
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    A trace theorem for solutions of linear partial differential equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 553-562 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we prove a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions, the trace of the solution on a codimension-one hypersuface will be just as regular as the solution itself. The proof is based on the Hörmander-Nirenberg pseudo-differential cut-off technique and a ‘fattening’ lemma, together with standard energy estimates.
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    Time decay of solutions of semilinear strongly damped generalized wave equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 427-443 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the asymptotic behaviour in time of the solutions of dissipative perturbations of wave-type equations in ∝N, utt + But + Au + G(u) = 0, with commuting positive operators A, B and a power like non-linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non-linear problems using the tools of scattering theory and the aforementioned conformal invariants.
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    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 461-481 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper.In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable.The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, the maximum and minimum velocities of a volleyball service.
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    Green's contact functions for heat conduction of two half-spaces and half-planes with application to several boundary contact problems (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 633-661 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Green's contact functions are constructed for two half-spaces and two half-planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.
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    Semigroup linearization for nonlinear parabolic equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 147-163 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an algorithm for nonlinear parabolic equations that uses a linear semigroup approach to decouple the nonlinearity, thus allowing simpler techniques to be used for the solution. The basic method is applicable only to a restricted class of problems, but can be extended with little loss of utility. Stability and error estimates are given, along with example computations.
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    Fourth-order finite difference scheme for a system of quasilinear elliptic equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 179-191 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The system of two quasilinear elliptic equations is approximated by the method of lines, which has the truncation error O(h2) at points neighboring the boundary and O(h4) at the most interior points. It is proved that the global error of the method is O(h4) at all mesh points. The two-point boundary value problem for the system of ordinary differential equations that arises from the method of lines is solved by the O(h4) convergent finite difference scheme, suitable to the equations of the form uxx = f(x, u) without the first derivative ux. The system of algebraic equations obtained by the full discretization is solved by Gauss elimination method for three diagonal matrices combined with the method of iterations. A numerical example is presented.
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    Superconvergence of recovered gradients of piecewise quadratic finite element approximations. Part II: L∞-error estimates (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 85-99 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 1 Ill.
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    Solving eigenvalue problems by implicit decomposition (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 113-145 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents three innovative methods for solving eigenvalue problems for differential equations based upon the techniques of implicit decomposition developed by Luo and Friedman. An eigenvalue problem can be written as an approximate algebraic system of the form [K]{X} + λ[M]{X} = 0 by employing finite elements. These methods provide robust techniques to compute the real eigenpair, λ and {X}, where [K] and [M] can be asymmetric, indefinite, and even singular.
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    Asymptotic factorization of evolution equations which involve linear operators (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 165-177 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Operator splitting for evolution equations which involve linear operators is investigated. A systematic method for identifying multifactor fractional-step operator splittings is proposed. The classical second-order accurate splittings of Strang readily emerge, as well as various third-order splittings of nonstandard type. Factorizations possessing mixed positive-negative fractional steps are discovered, as well as bizarre splittings whose factors include complex fractional steps. It is found that no higher-order accurate splitting which employs all positive fractional steps and which possesses less than nine operator factors can exist. For the linear case this implies second-order accurate splittings are optimal, as a further increase of one power in accuracy essentially requires a three-fold increase in work. This estimate slightly improves, for cases where the nonstandard splittings can be employed. Some numerical experiments which illustrate the theory are provided.
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    Numerical simulation of the turbulent boundary layer equations via a Runge-Kutta algorithm (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 375-384 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper addresses a hybrid computational procedure for the step-by-step calculation of momentum transfer in turbulent boundary layer flows along flat plates. The proposed procedure relies on a modified method of lines wherein transversal discretizations are carried out by a “control volume” being infinitesimal in the streamwise direction and finite in the transversal direction of the fluid flow. Using mixing length theory and coarse intervals in the transversal direction, the resulting system of ordinary differential equations of first order may be readily integrated on a personal computer utilizing a fourth-order Runge-Kutta algorithm. In general, a maximum number of sixteen lines is necessary at the trailing edge of the flat plate for a typical calculation. As a consequence, computing time and storage for each run were very small when compared to other finite-difference methods. Furthermore, to validate the hybrid procedure involving the method of lines and control volumes (MOLCV), comparisons with experimental data have been done in terms of both velocity distributions and local skin friction coefficients. For all cases tested, the proposed methodology predicts the growth of the boundary layer of gases correctly.
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    On the dynamics of a discrete reaction-diffusion system (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 385-405 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate various aspects of the dynamics of a discrete reaction-diffusion system. First, we examine the effect of the boundary conditions on the spatially uniform fixed point at locations far from the boundaries by using an asymptotic expansion. We show that, except for a few computational cells adjacent to the boundary, the fixed point practically coincides with the one calculated by using reflective boundary conditions (equivalent to an infinite domain). Next, we introduce a classification of the fixed points based on the wavelength in the infinite-medium approximation of the system. We use the symbolic manipulator MACSYMA to analytically calculate the amplitude of several such classes of fixed points and we generate bifurcation diagrams for their members. Also, we consider two special classes of periodic solutions; we calculate their amplitude analytically in the infinite-medium approximation, and generate bifurcation diagrams that shed new light on some previous confusing results. Finally, we present an analysis of fictitious periodic solutions that have been previously reported and incorrectly interpreted.
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    Discontinuous solutions to hyperbolic systems under operator splitting (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 277-297 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps exactly solves the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to “pseudo acoustic waves” and a nonphysical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed.
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    Masthead (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991) 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
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    Topics: Mathematics
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    A message to our readers (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. iii 
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    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Prismatic versus tetrahedral elements in three-dimensional finite element analyses of subsurface systems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 25-41 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A mesh of prismatic or tetrahedral elements automatically generated from an initial triangular grid is used to integrate 3-D flow equation in space. Many numerical comparisons between these two models have been performed. The results show that integration with tetrahedrons is as accurate as integration with prisms but much more efficient. The CPU time of solution with prismatic elements is about three times greater than that required employing tetrahedral elements.
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    An O(h6) cubic spline interpolating procedure for harmonic functions (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 43-59 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An O(h6) method for the interpolation of harmonic functions in rectangular domains is described and analyzed, The method is based on an earlier cubic spline technique [N. Papamichael and J.R. Whiteman, BIT 14, 452-459 (1974)], and makes use of recent results concerning the a posteriori correction of interpolatory cubic splines.
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    Masthead (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991) 
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    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Sensitivity analysis of partial differential equations: A case for functional sensitivity (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 101-112 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sensitivity analysis allows for analyzing the effects of parameter uncertainty. For functional parameters, the sensitivity of the system is described by the functional derivatives of the output variables with respect to the parameters. Approximation of each of the functional parameters by a finite number of scalars (via the finite element representation) allows one to use elementary sensitivity analysis. The functional sensitivities are easily approximated from elementary sensitivities and, being objective quantities, they allow one to evaluate the numerical quality of sensitivities. The grid density necessary for computing functional sensitivities may differ significantly from the grid required for the numerical solution of the governing equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070202
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    Influence matrix technique for the numerical spectral simulation of viscous incompressible flows (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 9-24 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A spectral algorithm based on the influence matrix technique is desclibed for solving numerically the flow of incompressible viscous fluids. The algorithmic development is for both Newtonian and non-Newtonian flows. To investigate the performance of the method several test problems are solved. Accurate results are obtained with relatively few degrees of freedom.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070103
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    Superconvergence of recovered gradients of piecewise quadratic finite element approximations. Part I: L2-error estimates (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 61-83 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence properties in the L2 norm are derived for the recovered gradients of piecewise quadratic finite element approximations on triangular partitions for two-dimensional elliptic problems and systems, including the case of linear elasticity. The analysis covers problems defined on polygonal domains, where the solutions have low regularity. The effects of numerical integration are treated.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070106
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    Masthead (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070301
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    Parallel finite element splitting-up method for parabolic problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 209-225 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.
    Additional Material: 4 Ill.
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    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
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    URL: http://dx.doi.org/10.1002/num.1690070304
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    Error bounds for numerical solution of partial differential equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 339-346 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070404
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    Finite element approach to the Stokes problem (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 363-374 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We approximate the Stokes problem by using a finite element method. This method utilizes the approach of Kleiser-Schumann, in which a boundary condition for the pressure is implicitly defined by a condition on the velocity. We consider a suitable splitting of the unknowns that allows one to reduce the Stokes problem to a cascade of classical Dirichlet problems and to a boundary integral equation.
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    URL: http://dx.doi.org/10.1002/num.1690070406
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    Masthead (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991) 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070101
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    Construction of a novel finite-difference scheme for a nonlinear diffusion equation (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 299-302 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A novel finite-difference scheme is constructed for a particular nonlinear diffusion equation. This scheme does not correspond to any of those that might be expected to follow from application of the standard procedures. A major advantage is that in the appropriate limit the difference equation model reduces to schemes that reproduce exactly the behaviors of the solution to the corresponding differential equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070307
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    Discrete least-squares global approximations to solutions of partial differential equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 303-315 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Solutions of partial differential equations (PDEs) using globally nonvanishing approximating functions are discussed, and the particular case of global polynomial solutions is studied. Convergence and error bounds are examined. Examples are given and compared with analytic solutions. This method seems particularly well suited for elliptic PDEs with continuous boundary conditions and nonhomogeneous terms, even for irregular domains, offering geometric convergence rates. By providing the minimized residues, strong error indicators are obtained. This algorithm's implementation retains simplicity under a variety of applications.
    Additional Material: 5 Ill.
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    Viscosity-splitting scheme for the Navier-Stokes equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 317-338 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A viscosity-splitting scheme for the initial boundary value problems of the Navier-Stokes equations is considered. In the scheme, the Stokes equation is solved in conjunction with a nonhomogeneous boundary condition which connects the tangent flow with a no-slip flow. Convergence is proved.
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    URL: http://dx.doi.org/10.1002/num.1690070403
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    Mixed methods and the marriage between “mixed” finite elements and boundary elements (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 347-362 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When fields that describe a physical situation extend over the whole space, but with complex behavior (nonlinearity, coupling, etc.) only in a bounded region and simple behavior in the rest of space, it may be worthwhile to treat the inner field by a finite elements procedure and the outer field by boundary elements. We address this “marriage” problem in the case of mixed elements. The model problem adopted for this discussion is magnetostatics. A new approach to the question of mixed elements is used, which emphasizes their parenthood with a classical concept of differential geometry, Whitney forms.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070405
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    Approximation of radial functions by piecewise polynomials on arbitrary grids (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 1-8 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the approximation of radial functions in IRN, N ≥ 2, by means of Lagrange finite elements on arbitrary grids. As an application, error estimates are obtained for the finite-element discretization of the radial Schrödinger equation. (AMS subject classification number: 65M60).
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    URL: http://dx.doi.org/10.1002/num.1690070102
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    Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 193-207 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070207
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    Fourth-order difference methods for the system of 2D nonlinear elliptic partial differential equations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 227-244 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present the fourth-order finite difference methods for the system of 2D nonlinear elliptic equations using 9-grid points on a square region R subject to Dirichlet boundary conditions. The method has been tested on viscous, incompressible 2D Navier-Stokes equations. The numerical results show that the proposed methods produce accurate and oscillation-free solutions for large Reynolds numbers.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/num.1690070303
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    Convergence of the contour dynamics methodThis work was done while the author was visiting the Laboratoire d'Analyse Numérique at the Université Pierre et Marie Curie, Paris. (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 261-276 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the contour dynamics method (CDM) is formulated and applied to the study of a two-dimensional incompressible and inviscid fluid flow. A result concerning the convergence of this method is proved. The foundation of the CDM is based on the study of the dynamic interaction between contours enclosing vortex regions. The idea of the analysis is to show that the CDM can be considered as a vortex filament method. Hence, the convergence for the contour dynamics method is proved by using some results in the theory of the vortex method.
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    URL: http://dx.doi.org/10.1002/num.1690070305
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