A Parameter-Uniform Numerical Method for a System of Singularly Perturbed Boundary Value Problems

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New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 177-187


Devendra Kumar

Department of Mathematics

Birla Institute of Technology & Science,

Pilani-333031,

India

mailto:dkumar2845@gmail.com






Abstract A parameter-uniform numerical method based on Shishkin mesh is constructed and analyzed for a weakly coupled system of singularly perturbed second order reaction-diffusion equations. A B-spline collocation method is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound (independent of the perturbation parameter ε) in the maximum norm is established theoretically. To illustrate the theoretical results, two test problems have been carried out.

Keywords Singular perturbation, Weakly coupled system, Boundary value problems, Boundary layer, B-spline collocation method.

Classification (MSC2000) 65L10, 65L11, 65L20, 65L60, 65D07.

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