IJASE  2018/01
Volume 15, No. 1 : 17-32
DOI:10.6703/IJASE.201802_15(1).017  
Fourth Order Numerical Method for Singularly Perturbed Delay Differential Equations

Gashu Gadisaa, Gemechis Filea* and Tesfaye Agaa
aDepartment of Mathematics, Jimma University, Jimma, Ethiopia


Abstract: This paper presents a numerical method to solve singularly perturbed delay differential equations. The solution of this problem exhibits layer or oscillatory behaviour depending on the sign of the sum of coefficients in reaction terms. A fourth order finite difference scheme on a uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) 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 four model examples. To show the accuracy of the method, the results are presented in terms of maximum absolute errors.

Keywords:  Singular perturbation; delay differential equation, boundary layer

 *Corresponding author; e-mail:  gammeef@yahoo.com
© 2018  Chaoyang University of Technology , ISSN 1727-2394