Fitted Second Order Scheme for Singularly Perturbed Differential-difference Equations

Lakshmi Sirisha¹ and Y.N. Reddy^1,

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

Cite this paper:
Lakshmi Sirisha and 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

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.

Keywords:
differential- difference equations central differences boundary layer

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