Insitute for Numerical Computation and Analysis
Preprints 1996

Preprints

  1. L.J. Crane, M.D. Gilchrist, J.J.H. Miller Analysis of Rayleigh-Lamb Scattering by a Crack in an Elastic Plate (not currently available)
  2. J.J.H. Miller, E. O'Riordan, G.I.Shishkin, Fitted Mesh Methods for the Singularly Perturbed Reaction Diffusion Problem, October 1996
    In this paper it is shown that a piecewise uniform mesh can be constructed on which the standard centered finite difference operator for this equation gives approximations which converge in the maximum norm to the exact solution, independently of the singular perturbation parameter. It is also shown that the piecewise linear interpolants of these approximations have the same property at each point of the domain.
  3. G.I.Shishkin, Finite Difference Approximations of Boundary Value Problems with Regular Boundary Layers, Part 3, November 1996
    Finite difference approximations of singularly perturbed boundary value problems for elliptic equations with regular boundary layers are considered. When a parameter multiplying the highest-order derivatives equals zero, the elliptic equations degenerate into first order equations. A method of constructing uniformly convergent (with respect to the singular perturbation parameter) finite difference schemes is presented. All the finite difference schemes presented here are monotonic. These schemes converge uniformly with first order accuracy.
  4. G.I.Shishkin, Finite Difference Approximations of Boundary Value Problems with Regular Boundary Layers, Parts 4 and 5, November 1996
    Finite difference approximations of singularly perturbed boundary value problems for elliptic equations with regular boundary layers are considered. When a parameter multiplying the highest-order derivatives equals zero, the elliptic equations degenerate into first order equations. A method of constructing uniformly convergent (with respect to the singular perturbation parameter) finite difference schemes is presented. All the finite difference schemes presented here are monotonic. These schemes converge uniformly with first order accuracy.
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    Paul A. Farrell/farrell@mcs.kent.edu