Solution of Singularly Perturbed Differential Difference Equations Using Higher Order Finite Differences

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. Solution of Singularly Perturbed Differential Difference Equations Using Higher Order Finite Differences. American Journal of Numerical Analysis. 2015; 3(1):8-17. doi: 10.12691/ajna-3-1-2

Abstract

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

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

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