High-order method for a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed type boundary conditions

Abstract

In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed type boundary conditions is considered. A robust-layer-resolving numerical method of high-order is suggested. An ?-uniform error estimates for the numerical solution and also to the numerical derivative are derived. Numerical results are presented, which are in agreement with the theoretical results. � 2012 Springer-Verlag.