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Tailored Finite Point Method for a Singular Perturbation Problem with Variable Coefficients in Two Dimensions

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Abstract

In this paper, 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 ε, 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.

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Authors and Affiliations

  1. Dept. of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Houde Han & Zhongyi Huang

Authors
  1. Houde Han
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  2. Zhongyi Huang
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Corresponding author

Correspondence to Zhongyi Huang.

Additional information

H. Han was supported by the NSFC Project No. 10471073.

Z. Huang was supported by the NSFC Project No. 10676017, the National Basic Research Program of China under the grant 2005CB321701.

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Han, H., Huang, Z. Tailored Finite Point Method for a Singular Perturbation Problem with Variable Coefficients in Two Dimensions. J Sci Comput 41, 200 (2009). https://doi.org/10.1007/s10915-009-9292-2

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  • DOI: https://doi.org/10.1007/s10915-009-9292-2

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