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.
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Rao, S.C.S., Kumar, S. & Kumar, M. A Parameter-Uniform B-Spline Collocation Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems. J Optim Theory Appl 146, 795–809 (2010). https://doi.org/10.1007/s10957-010-9683-4
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DOI: https://doi.org/10.1007/s10957-010-9683-4