IJPAM: Volume 88, No. 2 (2013)

HIGH ORDER METHOD FOR SINGULARLY PERTURBED
DIFFERENTIAL-DIFFERENCE EQUATIONS
WITH SMALL SHIFTS

A.A. Salama$^1$, D.G. Al-Amery$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Assiut University
Assiut, EGYPT


Abstract. This paper deals with a class of singularly perturbed differential-difference equations with small shifts (delay and advance). A high order accurate tridiagonal compact implicit method on non-uniform mesh is developed for approximating the solution of these equations. It is proved that the numerical method has third order of accuracy. The stability analysis and the truncation error are discussed. Several numerical examples are solved to demonstrate the accuracy and the efficiency of the proposed method and how the size of the delay and advance parameters affect the layer behavior of the solution.

Received: July 18, 2013

AMS Subject Classification: 65L10, 34K26, 76N20

Key Words and Phrases: singularly perturbed, differential-difference equations, high-order method, boundary layer, Shishkin mesh, small shifts

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DOI: 10.12732/ijpam.v88i2.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 2