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  • Articles  (46)
  • Numerical Methods  (46)
  • 1990-1994  (46)
  • 1993  (46)
  • Mathematics  (46)
  • 1
    Electronic Resource
    Electronic Resource
    Stability of some boundary value methods for the solution of initial value problems (1993)
    Springer
    BIT 33 (1993), S. 434-451 
    Details
    ISSN: 1572-9125
    Keywords: 34A50 ; 65L05 ; 65L20 ; Ordinary Differential Equations ; Initial Value Problems ; Numerical Methods ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability properties of three particular boundary value methods (BVMs) for the solution of initial value problems are considered. Our attention is focused on the BVMs based on the midpoint rule, on the Simpson method and on an Adams method of order 3. We investigate their BV-stability regions by considering the scalar test problem and constant stepsize. The study of the conditioning of the coefficient matrix of the discrete problem is extended to the case of variable stepsize and block ODE problems. We also analyse an appropriate choice for the stepsize for stiff problems. Numerical tests are reported to evidentiate the effectiveness of the BVMs and the differences among the BVMs considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990527
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  • 2
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993) 
    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.1690090301
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 191-211 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second-order accurate in time and of optimal accuracy in space in the L2 and H01 norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090207
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  • 4
    Electronic Resource
    Electronic Resource
    Premature in-bore separation of sabot-jacketed projectiles (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 225-234 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The premature separation of saboted projectiles undergoing high-mach-number in-bore acceleration is investigated. Results from a simplified numerical model for the problem are presented. Measured short-term velocity history for a typical projectile is used to describe the motion of a nonuniformly accelerating piston. Two numerical algorithms for calculating the shocked flow in tront of the accelerating piston are presented. Mach number and pressure time histories for the flow afford corrective input to the sabot design process. © 1993 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090303
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin method for a nonlinear parabolic-elliptic system with nonlinear mixed boundary conditions (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 235-259 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Materials which are heated by the passage of electricity are usually modeled by a nonlinear coupled system of two partial differential equations. The current equation is elliptic, while the temperature equation is parabolic. These equations are coupled one to another through the conductivities and the Joule effect. A computationally attractive discretization method is analyzed and shown to yield optimal error estimates in H1. © 1993 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090304
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  • 6
    Electronic Resource
    Electronic Resource
    Linearized stability analysis of staggered-grid difference schemes for multidimensional viscous incompressible flows (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 313-322 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a systematic linearized (frozen coefficient) von Neumann stability analysis for various staggered-grid marker-and-cell (MAC) finite difference schemes for solving viscous incompressible fluid flows. These schemes employ the primitive variables formulation and require the velocity field to be divergent free at every time step. It is illustrated that the stability results for staggered-grid MAC schemes are similar to that for the multidimensional convective-diffusion equation with constant coefficients. © 1993 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090308
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  • 7
    Electronic Resource
    Electronic Resource
    Existence and C0, α regularity of minima of a functional related to the grid-generation problem (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 261-264 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of C0,α regularity of minima of a functional arising from the grid-generation problem are provided in the case of n-dimensional domains. The functional studied in this article is a linear combination of the length functional, the volume functional, and a higher-order term. The inclusion of the latter guarantees the existence and regularity of a minimum via the direct method for calculus of variations. © 1993 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090305
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  • 8
    Electronic Resource
    Electronic Resource
    Positive solutions and dynamics of a finite difference reaction-diffusion system (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 285-311 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction-diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction-diffusion problem. © 1993 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090307
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  • 9
    Electronic Resource
    Electronic Resource
    Three-dimensional singularities of elastic fields near vertices (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 323-337 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the computation of the singular behavior of an elastic field near a three-dimensional vertex subject to displacement boundary conditions we use a boundary integral equation of the first kind whose unknown is the boundary stress. Localization at the vertex and Mellin transformation yield a one-dimensional integral equation on a piecewise circular curve γ in IR3 depending holomorphically on the complex Mellin parameter. The corresponding spectral points and packets of generalized eigenvectors characterize the desired stress field and are computed by a spline-Galerkin method with graded meshes at the corner points of the curve γ. © 1993 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090309
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  • 10
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993) 
    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.1690090401
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