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

S. C. S. Rao (), S. Kumar and M. Kumar
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S. C. S. Rao: Indian Institute of Technology Delhi
S. Kumar: Indian Institute of Technology Delhi
M. Kumar: Indian Institute of Technology Delhi

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 3, No 13, 795-809

Abstract: 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 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-010-9683-4

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