A Numerical Method for Singularly Perturbed Convection-diffusion Problems Posed on Smooth Domains

Abstract A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed the data so that only regular exponential boundary layers appear in solution. domain decomposition used, which uses a rectangular grid outside layer and Shishkin mesh, aligned curvature of outflow boundary, near layer. Numerical results presented demonstrate effectiveness proposed numerical algorithm.