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High-accuracy quadrature methods for solving nonlinear boundary integral equations of axisymmetric Laplace’s equation

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Abstract

In this article, we study the numerical solutions of axisymmetric Laplace’s equation with nonlinear boundary conditions. The problem could be converted into nonlinear boundary integral equations by the ring potential theory. The mechanical quadrature method is presented for solving the equations, which possesses high-accuracy order of O(h3) and low computing complexities. Using the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with odd powers is obtained. Moreover, the Richardson’s extrapolation algorithm is used to improve the accuracy order of O(h5). The efficiency of the algorithm is illustrated by numerical examples.

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Acknowledgements

The authors are grateful to the YJRC Program (YJRC2018-1) of Chengdu Normal University and the National Natural Science Foundation of China (11371079) for financial funding.

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Authors and Affiliations

  1. School of Mathematics, Chengdu Normal University, Chengdu, 611130, China

    Hu Li

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Jin Huang

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  1. Hu Li
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  2. Jin Huang
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Correspondence to Hu Li.

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Communicated by Jose Alberto Cuminato.

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Li, H., Huang, J. High-accuracy quadrature methods for solving nonlinear boundary integral equations of axisymmetric Laplace’s equation. Comp. Appl. Math. 37, 6838–6847 (2018). https://doi.org/10.1007/s40314-018-0714-3

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  • DOI: https://doi.org/10.1007/s40314-018-0714-3

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