A Hybrid Numerical Scheme For Solving Singularly Perturbed Convection-Diffusion Problems With Discontinuous Terms

Abstract

This thesis presents a hybrid numerical scheme for solving singularly perturbed convection- diffusion boundary value problems with discontinuous convection coefficient and source terms. A hybrid numerical scheme was constructed using the non-standard finite-difference method on the Shishkin mesh and midpoint upwind finite difference schemes. The solutions of the problem considered exhibits an interior layer. Stability and uniform convergence analysis are investigated for the proposed hybrid scheme. Maximum absolute errors and convergence rates are computed for various perturbation parameter values and mesh sizes, using two numerical test examples. The proposed scheme is shown to be almost first-order uniformly convergent.