A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

Author:

Erdogan Fevzi1,Sakar Mehmet Giyas1,Saldır Onur1

Affiliation:

1. Department of Mathematics, Faculty of Science , Van Yuzuncu Yil University , Van Turkey

Abstract

Abstract The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

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