An improved Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems
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 ( ln ε ) 2 N − 1 ), where ε is the perturbation parameter and N is the number of mesh steps. The high accuracy of the method is illustrated by numerical examples.
Vulanović, R., & Nhan, T. A. (2021). An improved Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems. Applied Numerical Mathematics, 170, 128–145. https://doi.org/10.1016/j.apnum.2021.07.019