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

Abstract

This article presents a numerical method to solve singularly perturbed turning point problems exhibiting two exponential boundary layers. Classical finite-difference schemes do not yield parameter uniform convergent results on a uniform mesh, in general (Robust Computational Techniques for Boundary Layers, Chapman & Hall, London, CRC Press, Boca Raton, FL, 2000). In order to overcome this difficulty, we propose an appropriate piecewise uniform (Shishkin) mesh and apply the classical finite-difference schemes on this mesh. Error estimates are derived by decomposing the solution into smooth and singular components. The present method is layer resolving as well as parameter uniform convergent. Numerical examples are presented to show the applicability and efficiency of the method.