A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term

Authors:
A. Tamilselvan;N. Ramanujam;V. Shanthi
Affiliations:
Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India;Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India;Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, a numerical method based on finite difference scheme and Shishkin mesh for singularly perturbed two second order weakly coupled system of ordinary differential equations with discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.