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http://dx.doi.org/10.14317/jami.2013.131

AN INITIAL VALUE TECHNIQUE FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH A SMALL NEGATIVE SHIFT  

Rao, R. Nageshwar (Department of Mathematics, Visvesvaraya National Institute of Technology)
Chakravarthy, P. Pramod (Department of Mathematics, Visvesvaraya National Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.31, no.1_2, 2013 , pp. 131-145 More about this Journal
Abstract
In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.
Keywords
Initial value technique; singular perturbation; differential-difference equation; boundary layer;
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