Parameter Uniform Numerical Method for a Weakly Coupled System of Second Order Singularly Perturbed Turning Point Problem with Robin Boundary Conditions

In this paper, a parameter uniform numerical method for a weakly coupled system of two second order singularly perturbed turning point problems with Robin boundary conditions is presented. 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 and it is of order O(N−1lnN). Numerical examples are given which validate theoretical results.