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The Linear Barycentric Rational Quadrature Method for Auto-Convolution Volterra Integral Equations

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Abstract

This paper is concerned with the numerical solution of auto-convolution Volterra integral equations. A composite quadrature method based on linear barycentric rational interpolation is introduced. The method is easy to be implemented because only a linear equation needs to be solved in each time step. Collocation method is used as the starting procedure. The boundedness and convergence of the numerical solution are studied in detail. Some numerical experiments are carried out to confirm the theoretical results.

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Acknowledgements

The authors would like to thank Dr. Zhanwen Yang for his helpful suggestions for the Proof of Theorem 2. They are also grateful to the anonymous referees and the editors whose comments improved the paper significantly.

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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

Authors
  1. Min Li
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  2. Chengming Huang
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Corresponding author

Correspondence to Chengming Huang.

Additional information

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

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Li, M., Huang, C. The Linear Barycentric Rational Quadrature Method for Auto-Convolution Volterra Integral Equations. J Sci Comput 78, 549–564 (2019). https://doi.org/10.1007/s10915-018-0779-6

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  • DOI: https://doi.org/10.1007/s10915-018-0779-6

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