A parameter robust second order numerical method for a singularly perturbed two-parameter problem

被引：74
作者：
Gracia, JL
O'Riordan, E [1 ]
Pickett, ML
机构：
[1] Dublin City Univ, Sch Math Sci, Dublin 9, Ireland
[2] Univ Zaragoza, Dept Matemat Aplicada, Zaragoza, Spain
来源：
APPLIED NUMERICAL MATHEMATICS | 2006年 / 56卷 / 07期
关键词：
singular perturbation; uniform convergence; Shishkin mesh; second order;
D O I：
10.1016/j.apnum.2005.08.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The monotone operator is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound in the maximum norm is established theoretically whose error constants are shown to be independent of both singular perturbation parameters. Numerical results are presented which support the theoretical results. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
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收藏
页码：962 / 980
页数：19
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