Journal of Optimization Theory and Applications

, Volume 146, Issue 3, pp 795–809 | Cite as

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

Article

Abstract

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 ε in the maximum norm. Numerical results are presented to validate the theoretical results.

Keywords

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

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology DelhiHauz KhasIndia

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