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M. K. Kadalbajoo and K. K. Sharma, -Uniform fitted mesh method for Singularly Perturbed Differential-Difference Equations: Mixed type of shifts with layer behaviour, International Journal of Computation Mathematics, 81 2004, 49-62.

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Article

Fitted Second Order Scheme for Singularly Perturbed Differential-difference Equations

1Department of Mathematics, National Institute of Technology, WARANGAL, India


American Journal of Numerical Analysis. 2014, Vol. 2 No. 5, 136-143
DOI: 10.12691/ajna-2-5-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lakshmi Sirisha, Y.N. Reddy. Fitted Second Order Scheme for Singularly Perturbed Differential-difference Equations. American Journal of Numerical Analysis. 2014; 2(5):136-143. doi: 10.12691/ajna-2-5-1.

Correspondence to: Y.N.  Reddy, Department of Mathematics, National Institute of Technology, WARANGAL, India. Email: ynreddy_nitw@yahoo.com

Abstract

In this paper, we present a fitted second order stable central finite difference scheme for solving singularly perturbed differential-difference equations (with delay and advanced parameter). First, the given second order differential difference equation is replaced by an asymptotically equivalent second order singularly perturbation problem. Then, a fitting factor is introduced into the second order stable central difference scheme and determined its value from the theory of singular perturbations. Discrete Invariant Imbedding Algorithm is used to solve the resulting tri-diagonal system. The error analysis and convergence of the scheme are also discussed. To validate the applicability of the method, several model examples have been solved by taking different values for the delay parameter δ, advanced parameter ηand the perturbation parameter ε.

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