A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Cen, Zhongdi¹  Xu, Aimin¹  Le, Anbo¹ 

[1] Zhejiang Wanli Univ, Inst Math, Ningbo 315100, Zhejiang, Peoples R China

关键词: Singular perturbation;    Hybrid finite difference scheme;    Shishkin mesh;    Uniform convergence;   

DOI  :  10.1016/j.cam.2010.05.006

来源: Elsevier

【 摘 要 】

A system of coupled singularly perturbed initial value problems with two small parameters is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solution of the system has boundary layers that overlap and interact. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh a hybrid finite difference scheme is proved to be almost second-order accurate, uniformly in both small parameters. Numerical results supporting the theory are presented. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free