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Barycentric rational collocation methods for Volterra integral equations with weakly singular kernels

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Abstract

In this paper, we investigate barycentric rational collocation methods for weakly singular Volterra integral equations. Since the exact solution usually has a weak singularity at the initial point, a smoothing transformation is first used to convert the original equation to a new equation whose exact solution is smooth enough. Then, by the collocation approach based on barycentric rational interpolation, a discrete numerical scheme is constructed, and a general convergence result is established. Finally, the theoretical results are illustrated by some numerical examples.

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Acknowledgements

The authors are grateful to the anonymous referees and the editors for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Min Li & Chengming Huang

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Chengming Huang

  3. School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, China

    Wanyuan Ming

Authors
  1. Min Li
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  2. Chengming Huang
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  3. Wanyuan Ming
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Correspondence to Chengming Huang.

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Communicated by Hui Liang.

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This work was supported by National Natural Science Foundation of China (No. 11771163).

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Li, M., Huang, C. & Ming, W. Barycentric rational collocation methods for Volterra integral equations with weakly singular kernels. Comp. Appl. Math. 38, 120 (2019). https://doi.org/10.1007/s40314-019-0890-9

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  • DOI: https://doi.org/10.1007/s40314-019-0890-9

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