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Reproducing Kernel Method for Singularly Perturbed One-Dimensional Initial-Boundary Value Problems with Exponential Initial Layers

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Abstract

In this paper, a meshless numerical method is proposed for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. The method is a combination of the domain decomposition method and the reproducing kernel method. A fitted reproducing kernel is constructed for initial layer domain problem. Some numerical results confirming the expected behavior of the method are shown.

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Authors and Affiliations

  1. Department of Mathematics, Changshu Institute of Technology, Suzhou, 215500, Jiangsu, China

    Fazhan Geng & Zhiqiang Tang

  2. School of Sciences, Hebei University Technology, Tianjin, 300130, China

    Yongfang Zhou

Authors
  1. Fazhan Geng
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  2. Zhiqiang Tang
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  3. Yongfang Zhou
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Correspondence to Fazhan Geng.

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Geng, F., Tang, Z. & Zhou, Y. Reproducing Kernel Method for Singularly Perturbed One-Dimensional Initial-Boundary Value Problems with Exponential Initial Layers. Qual. Theory Dyn. Syst. 17, 177–187 (2018). https://doi.org/10.1007/s12346-017-0242-3

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  • DOI: https://doi.org/10.1007/s12346-017-0242-3

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