An almost fourth order uniformly convergent
difference scheme for a semilinear
singularly perturbed reaction-diffusion problem |
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Authors: | Guangfu Sun Martin Stynes |
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Institution: | (1) Department of Mathematics, University College, Cork, Ireland e-mail address:stynes@.ucc.ie , IE |
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Abstract: | Summary.
This paper is concerned with a high order convergent
discretization for the semilinear reaction-diffusion problem:
,
for , subject to ,
where .
We assume that on
, which
guarantees uniqueness of a solution to
the problem. Asymptotic properties of
this solution are discussed. We consider a
polynomial-based three-point
difference scheme on a simple piecewise
equidistant mesh of Shishkin type.
Existence and local uniqueness of a solution
to the scheme are analysed. We
prove that the scheme is almost fourth order
accurate in the discrete maximum
norm, uniformly in the perturbation parameter
. We present numerical
results in support of this result.
Received February 25, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 34E15 65L10 65L12 65L50 |
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