A FITTED NUMERICAL TECHNIQUE FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITION

A FITTED NUMERICAL TECHNIQUE FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITION

M. A. Ayele, A. A. E Tiruneh, G. A. Derese

[PDF]

Abstract

In this paper, we present a  tted numerical scheme for singularly perturbed delay di erential equations with integral boundary conditions. To develop the scheme, the exact and approximate rules of integration with  nite di erence approximations of the  rst derivative are used. In the developed scheme, a  tting factor is introduced whose value is evaluated from the theory of singular perturbation. The Runge{Kutta method of order four is used to solve the reduced problem, and for the integral boundary condition, Composite Simpson's rule of integration is applied. The proposed method is shown to be second-order convergent. Numerical illustrations for various values of perturbation parameters are presented to validate the proposed method. The numerical results clearly show the high accuracy and order of convergence of the proposed scheme as compared to some of the results available in the literature.

Keywords

Singular perturbation, delay di erential equations, integral boundary, numerical integration