An improved Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems

摘要

We consider the Kellogg-Tsan decomposition of the solution to the linear one-dimensional singularly perturbed convection-diffusion problem and improve it by including the solution of the corresponding reduced problem as a component. The upwind scheme on a modified Shishkin-type mesh is used to approximate the unknown component of the decomposition. It is proved that the error is O (ε(lnε)~2N~(-1)), where e is the perturbation parameter and N is the number of mesh steps. The high accuracy of the method is illustrated by numerical examples.