Non-Polynomial Cubic Spline Method for Solving Singularly Perturbed Delay Reaction-Diusion Equations

Bekele Badada Tirfesa, Gemechis File Duressa, Habtamu Garoma Debela

Abstract

In this paper, non-polynomial cubic spline method for solving singularly perturbed delay reaction- diusion equations with twin layers and oscillatory behavior has been presented. In this method, the second order singularly perturbed delay reaction-diusion equation transformed into an asymptotically equivalent singularly perturbed two point boundary value problem using Taylor series expansion. Then, non-polynomial cubic spline approximations are developed into a three-term recurrence relation, which has solved using Thomas Algorithm. The stability and convergence of the method have been established. The applicability of the proposed method is validated by implementing it by four model examples without exact solutions for dierent values of the perturbation parameter " and delay parameter .