A Parameter-Uniform B-Spline Collocation Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems

被引：14

作者：

Rao, S. C. S. ^{[1
]}

Kumar, S. ^{[1
]}

Kumar, M. ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, New Delhi, India

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2010年 / 146卷 / 03期

关键词：

Singular perturbation; Reaction-diffusion problems; B-spline collocation method; Shishkin mesh; GRIDS;

D O I：

10.1007/s10957-010-9683-4

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider a Dirichlet boundary value problem for a class of singularly perturbed semilinear reaction-diffusion equations. A B-spline collocation method on a piecewise-uniform Shishkin mesh is developed to solve such problems numerically. The convergence analysis is given and the method is shown to be almost second-order convergent, uniformly with respect to the perturbation parameter e in the maximum norm. Numerical results are presented to validate the theoretical results.

引用

页码：795 / 809

页数：15

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