Multiscale convection in one dimensional singularly perturbed convection-diffusion problems

Abstract

Linear singularly perturbed ordinary differential equations of convection diffusion type are considered. The convective coefficient varies in scale across the domain which results in interior layers appearing in areas where the convective coefficient decreases from a scale of order one to the scale of the diffusion coefficient. Appropriate parameter-uniform numerical methods are constructed. Numerical results are given to illustrate the theoretical error bounds established. © 2013 Springer-Verlag.