ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION TYPE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITION

This paper presents the study of singularly perturbed differential equations of convection diffusion type with non-local boundary condition. The proposed numerical scheme is a combination of classical finite difference method for the initial boundary condition and nonstandard finite difference method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order convergence independent of the perturbation parameter ε.