Solving SPDDE using fourth order numerical method

Abstract

In this paper we present a fourth order numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer behaviour at one end. A fourth order finite difference scheme on a uniform mesh is developed. The effect of delay and advance parameters on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on model examples. To show the accuracy of the method, the results are presented in terms of maximum absolute errors.