Insitute for Numerical Computation and Analysis
Preprints 1996

Preprints

  1. H. MacMullen, J.J.H. Miller, E. O'Riordan, G.I.Shishkin,
    A second order parameter-robust overlapping Schwartz method for reaction-diffusion problems with boundary layers., November 1997
    postscript version (826601 bytes)| pdf version(313284 bytes)
    In this paper a singularly perturbed self-adjoint ordinary differential equation is examined. It is shown that a suitably designed Schwartz method, based on a standard finite difference operator on uniform meshes, gives approximations which converge in the maximum norm to the exact solution, independently of the singular perturbation parameter. The convergence is shown to be essentially second order uniformly with respect to the singular perturbation parameter. Numerical results are presented, which validate the theoretical results.
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    Paul A. Farrell/farrell@mcs.kent.edu