Second-order Numerical Scheme for Singularly Perturbed Reaction – Diffusion Robin Problems

Date of Online Publication: 27/10/2007
Keywords: Second-order Numerical Scheme for Singularly Perturbed, Singular perturbation problems, Robin boundary conditions, cubic spline, piecewise-uniform Shishkin mesh, error analysis.
Authors: Srinivasan Natesan and Rajesh K. Bawa
Pages: 177-192
In this article, we consider singularly perturbed reaction-diffusion Robin boundary-value problems. To solve these problems we construct a numerical method which involves both the cubic spline and classical finite difference schemes. The proposed scheme is applied on a piece-wise uniform Shishkin mesh. Truncation error is obtained, and the stability of the method is analyzed. Also, parameter-uniform errors estimates are derived. Three test problems are experimented.

 

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