A Uniformly Convergent Scheme for A System of Two Coupled Singularly Perturbed Reaction-Diffusion Robin Type Boundary Value Problems with Discontinuous Source Term

Pathan Mahabub Basha^1, and Vembu Shanthi¹

¹Department of Mathematics, National Institute of Technology, Tiruchirappalli, India

Cite this paper:
Pathan Mahabub Basha and Vembu Shanthi. A Uniformly Convergent Scheme for A System of Two Coupled Singularly Perturbed Reaction-Diffusion Robin Type Boundary Value Problems with Discontinuous Source Term. American Journal of Numerical Analysis. 2015; 3(2):39-48. doi: 10.12691/ajna-3-2-2

Abstract

In this paper, a uniformly convergent scheme for a system of two coupled singularly perturbed reaction-diffusion Robin type mixed boundary value problems (MBVPs) with discontinuous source term is presented. A fitted mesh method has been used to obtain the difference scheme for the system of MBVPs on a piecewise uniform Shishkin mesh. A cubic spline scheme is used for Robin boundary conditions and the classical central difference scheme is used for the differential equations at the interior points. An error analysis is carried out and numerical results are provided to show that the method is uniformly convergent with respect to the singular perturbation parameter which supports the theoretical results.

Keywords:
singular perturbation problem weakly coupled system discontinuous source term Robin boundary conditions Shishkin mesh fitted mesh method uniform convergence

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