IJPAM: Volume 73, No. 4 (2011)

NUMERICAL METHOD FOR SINGULARLY PERTURBED
DIFFERENTIAL-DIFFERENCE EQUATIONS
WITH TURNING POINT

Pratima Rai$^1$, Kapil K. Sharma$^2$
$1,2$Department of Mathematics
Center for Advance Study in Mathematics
Panjab University
Chandigarh, 160014, INDIA


Abstract. In this paper, we present a numerical method to solve boundary value problems for singularly perturbed differential-difference equations with turning point. A singularly perturbed differential-difference equation is a differential equation in which the highest order derivative is multiplied by a small parameter and involving at least one delay term . The points of the domain where the coefficient of the convection term in the singularly perturbed differential equation vanishes are known as the turning points. The solution of such type of differential equations exhibits boundary layer(s) or interior layer(s) depending upon the nature of the convection and the reaction term. In the development of numerical scheme for singularly perturbed differential-difference equations with turning point, we use a scheme based on El-Mistikawy Werle exponential finite difference scheme [#!mist!#]. Some a priori estimates have been established to prove the convergence and stability of the proposed scheme.

Received: July 3, 2011

AMS Subject Classification: 65L12, 34K26, 34K28

Key Words and Phrases: singular perturbations, differential-difference equations, turning point, interior layer, fitted operator methods ODE

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 4