Fitted non-polynomial cubic spline method for singularly perturbed delay convection-diffusion equations

Abstract

This paper presents a fitted non-polynomial cubic spline method for solving singularly perturbed delay differential equations with left and right end layers for which a small delay parameter is in the convection term. The stability and convergence of the method have been established. To validate the applicability of the proposed method two model examples without exact solution have been considered and solved for different values of the perturbation parameter and mesh sizes. Both theoretical error bounds and numerical rate of convergences have been investigated for the proposed method and observed to be in agreement. The numerical results have been tabulated and further to examine the effect of delay parameter on the boundary layer solution, graphs have been given for different values of delay parameter.