A novel mathematical modeling of multiple scales for a class of two dimensional singular perturbed problems

Abstract

A novel mathematical modeling of multiple scales (NMMMS) is presented for a class of singular perturbed problems with both boundary or transition layers in two dimensions. The original problems are converted into a series of problems with different scales, and under these different scales, each of the problem is regular. The rational spectral collocation method (RSCM) is applied to deal with the problems without singularities. NMMMS can still work successfully even when the parameter ε is extremely small ( ε = 10 −25 or even smaller). A brief error estimate for the model problem is given in Section 2. Numerical examples are implemented to show the method is of high accuracy and efficiency.