AN EFFICIENT NUMERICAL TECHNIQUE FOR THE SOLUTION OF SONGULARLY PERTURBED CONVECTION DIFFUSION EQUATION WITH SHIFT OPERATOR

Abstract

The thesis presents a numerical approach to solving second-order ordinary differential equation boundary value problems with singularly perturbed convection diffusion, where a small parameter is multiplied by the largest derivative ϵ with Dirichlet’s boundary conditions. In order to solve these dif ferential equation we use the upwind finite difference method including uniform mesh and the piecewise uniform mesh introduced by Ivanovich Shishkin. The convergence between the analytic solution and the solution obtained from the numerical approach of the simple Convection Diffusion Problem are provided. Also we analyze this problem with delay and advance parameters. This paper presents the numerical outcomes displayed as tables and graphs, showing that our suggested approach provides a very accurate approximation of the exact solution.