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Zbl 1203.65225
Han, Houde; Huang, Zhongyi
Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensions. (English)
[J] J. Sci. Comput. 41, No. 2, 200-220 (2009). ISSN 0885-7474; ISSN 1573-7691/e

Summary: We propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small $\epsilon $, i.e. the boundary layers and interior layers do not need to be resolved numerically. In our numerical implementation, we study the classification of all the singular points for the corresponding degenerate first order linear dynamic system. We also study some cases with nonlinear coefficients. Our tailored finite point method is very efficient in both linear and nonlinear coefficients cases.

MSC 2000:: *65N08

Keywords: tailored finite point method; singular perturbation problem; singular point

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