Numerical Solution of Singularly Perturbed Differential-Difference Equations with Dual Layer

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. Numerical Solution of Singularly Perturbed Differential-Difference Equations with Dual Layer. American Journal of Applied Mathematics and Statistics. 2014; 2(5):336-343. doi: 10.12691/ajams-2-5-7

Abstract

In this paper, we discuss the numerical solution of singularly perturbed differential-difference equations exhibiting dual layer behavior. First the second order singularly perturbed differential-difference equation is replaced by an asymptotically equivalent second order singularly perturbed ordinary differential equation. Then, second order stable central difference scheme has been applied to get a three term recurrence relation which is easily solved by Discrete Invariant Imbedding Algorithm. Some numerical examples have been considered to validate the computational efficiency of the proposed numerical scheme. To analyze the effect of the parameters on the solutions, the numerical solutions have also been plotted using graphs. The error bound and convergence of the method have also been established.

Keywords:
singular perturbations differential-difference equations dual layer delay parameter advance parameter

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