Numerical Analysis and Applicable Mathematics
Title
Fitted Numerical Method for Singularly Perturbed Delay Differential Equations
Authors
Gemechis File Duressa*a and Habtamu Garoma Debelaa
aDepartment of Mathematics, College of Natural Sciences, Jimma University, Jimma, Ethiopia.
*Corresponding author E-mail address: gammeef@gmail.com (Gemechis File Duressa)
Article History
Publication details: Received: 17th May 2020; Revised: 14th June 2020; Accepted: 15th June 2020; Published: 26th June 2020
Cite this article
Duressa G. F.; Debela H. G. Fitted Numerical Method for Singularly Perturbed Delay Differential Equations. Numer. Anal. Appl. Math., 2020, 1(1), 45-56.
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 the coefficients in reaction terms. A fourth order fitted numerical scheme on 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. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.
Keywords
Singular perturbation; Delay differential equation; Fitted operator; Twin layers; Oscillatory layers
