Numerical method for a system of second order singularly perturbed turning point problems

Document Type: Research Paper

Authors

1 Department of Mathematics, Bharathidasan University, Tamilnadu, India

2 Department of Mathematics, St. Joseph's college, Tamilnadu, India

Abstract

In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on this mesh. An error estimate is derived by using supremum norm which is $O(N^{-1}(\ln N)^2)$. Numerical examples are given to validate theoretical results.

Keywords