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.
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页码：795 / 809
页数：15
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