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  • Mathematics and Statistics  (340)
  • Wiley-Blackwell  (340)
  • 1985-1989  (340)
  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070101
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  • 2
    Electronic Resource
    Electronic Resource
    Finite elements for the eigenvalue problem of differential operators in unbounded intervals (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 1-39 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The eigenvalue problem for one-dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non-pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070102
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  • 3
    Electronic Resource
    Electronic Resource
    Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 40-54 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves.The well-known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iωE = 0, rotE - iωH = 0, with n × E prescribed on the boundary. The same result holds for the “Mie-potentials”Which can be proved by a Lemma of Mie [6].Two numerical examples for the three-dimensional boundary value problems (field of a dipole, field of reflection) are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070103
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  • 4
    Electronic Resource
    Electronic Resource
    On spline collocation methods for boundary integral equations in the plane (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 74-89 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Nowadays boundary elemen; methods belong to the most popular numerical methods for solving elliptic boundary value problems. They consist in the reduction of the problem to equivalent integral equations (or certain generalizations) on the boundary Γ of the given domain and the approximate solution of these boundary equations. For the numerical treatment the boundary surface is decomposed into a finite number of segments and the unknown functions are approximated by corresponding finite elements and usually determined by collocation and Galerkin procedures. One finds the least difficulties in the theoretical foundation of the convergence of Galerkin methods for certain classes of equations, whereas the convergence of collocation methods, which are mostly used in numerical computations, has yet been proved only for special equations and methods.In the present paper we analyse spline collocation methods on uniform meshes with variable collocation points for one-dimensional pseudodifferential equations on a closed curve with convolutional principal parts, which encompass many classes of boundary integral equations in the plane. We give necessary and sufficient conditions for convergence and prove asymptotic error estimates. In particular we generalize some results on nodal and midpoint collocation obtained in [2], [7] and [8].The paper is organized as follows. In Section 1 we formulate the problems and the results, Section 2 deals with spline interpolation in periodic Sobolev spaces, and in Section 3 we prove the convergence theorems for the considered collocation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070105
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  • 5
    Electronic Resource
    Electronic Resource
    Stabilization and regularization for solutions of an ill posed problem for the wave equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 202-209 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the problem of finding u: [O, T] → D(A), D(A) ⊆ H, H a Hibert space such that:Is a linear positive, self-adjoint operator with a compact inverse. The problem is well known to be illposed because uniqueness and existence generally fail. We restore the stability with an a priori bound on ∥ du(0)/dt ∥ for some particular values of T.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070112
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  • 6
    Electronic Resource
    Electronic Resource
    Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 210-222 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity.Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309-318) who obtained such results for the eigenvalues of the fixed membrane problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070113
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  • 7
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070114
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  • 8
    Electronic Resource
    Electronic Resource
    On the swelling of a glassy polymer in contact with a well-stirred solvent (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 238-250 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a free boundary problem arising from a model for sorption of solvent by polymers.Existence and uniqueness of the solution are proved and some results about the asymptotic behaviour are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070115
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  • 9
    Electronic Resource
    Electronic Resource
    Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 251-259 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ∂Ω which are arbitrary, radial, or ν-directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠-convex annular domain. We apply these results to some free-boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070116
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  • 10
    Electronic Resource
    Electronic Resource
    An integral equation of elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 261-268 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work a certain mixed problem in R+3 for the Lamé equations in the theory of elasticity is reduced to the integral equationAn explicit formula for the solutions is given for either Ω = {x:x2 〉 0} or Ω = {x:∥x∥〈r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥〈r} are found in [5], [4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070117
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