Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers

Abstract

In this paper, a numerical method based on Shishkin mesh for a singularly perturbed fourth order differential equation with a turning point exhibiting boundary layers is presented. In this method the problem is transformed into a weakly coupled system of two second order equations, one without the parameter ε and the other with the parameter ε multiplying the highest derivative with suitable boundary conditions. We apply classical finite difference scheme on an appropriate piecewise uniform (Shishkin) mesh. Parameter uniform error bounds for the numerical solution are established. Numerical results are provided to illustrate the theoretical results. Keywords: Singularly perturbed turning point problems, Finite difference scheme, Shishkin mesh