Special Fitted Finite Difference Scheme for Delay Differential Equation With Dual Boundary Layers

Abstract

In this paper, we have proposed a fitted special finite difference method for the solution of delay differential equations with dual boundary layers. The delay differential equation is replaced by an asymptotically equivalent singular perturbation problem using the Taylor's series expansion. Then, a fitted special finite difference scheme is described to get accurate solution to the problem. The method is demonstrated by implementing on several model problems by taking various values for the delay parameter \(\delta\) and perturbation parameter \(\varepsilon \). To show the effect of delay on the boundary layer or oscillatory behaviour of the solution, several numerical problems are carried out in this article. To demonstrate the effect on the layer behaviour, the solution of the problems are shown graphically. We observed that when the order of the coefficient of the delay parameter is of \(o(1)\), the delay affects the boundary layer solution but maintains the layer behaviour and as the delay increases, the thickness of the left boundary layer decreases while that of the right boundary layer increases.