Fourth Order Exponentially Fitted Finite Difference Method for Solving Singularly Perturbed Delay Differential Equation Involving Two Small Parameters

Abstract

This thesis presents exponentially fitted finite difference method to solve singularly perturbed delay differential equation involving two small parameters. A fourth order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on two model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.