Fitted Fourth Order Scheme for Singularly Perturbed Delay Convection-Diffusion Equations

Abstract

This paper presents a fitted fourth order numerical scheme for solving singularly perturbed convection-diffusion equations. The obtained scheme is transformed into a three-term recurrence relation and solved by Thomas algorithm. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results and also to know the behavior of the solution in the boundary layer for perturbation parameter  is less than mesh size h. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.

Keywords: Boundary layer; Convection-diffusion equation; Singularly perturbed; Stability