Asymptotic Initial-Value Method for Second-Order Singular Perturbation Problems of Reaction-Diffusion Type with Discontinuous Source Term

被引：0
作者：
T. Valanarasu
N. Ramanujam
机构：
[1] Bharathidasan University,Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2007年 / 133卷
关键词：
Singular perturbation problems; Discontinuous source terms; Boundary and interior layers; Asymptotic expansion approximations; Boundary value problems; Initial value problems; Initial value methods;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a numerical method is presented to solve singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations with a discontinuous source term. First, an asymptotic expansion approximation of the solution of the boundary-value problem is constructed using the basic ideas of the well-known WKB perturbation method. Then, some initial-value problems and terminal-value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial-value problems and terminal-value problems are singularly-perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples are provided to illustrate the method.
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页码：371 / 383
页数：12
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