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Error asymptotic expansion for the numerical approximation of logarithmic-kernel integral equations on closed curves

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Abstract

We present a modified quadrature method to solve the logarithmic-kernel integral equations, because of its importance in mathematical physics. At first, the quadrature method is constructed by the trapezoidal rule, which is used to discrete the integral equation. In addition, when the integral curve can be represented by a periodic function, the error asymptotic expansion with single parameter will be proved, which shows that the quadrature method has high accuracy order \(O(h^3)\), and can improve the accuracy of numerical solutions to \(O(h^5)\) order accuracy by extrapolation algorithm once. Three numerical examples show our theoretical analysis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (12101089) and the Natural Science Foundation of Sichuan Province (2022NSFSC1844).

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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 José R Fernández.

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Li, H., Huang, J. Error asymptotic expansion for the numerical approximation of logarithmic-kernel integral equations on closed curves. Comp. Appl. Math. 42, 229 (2023). https://doi.org/10.1007/s40314-023-02361-3

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  • DOI: https://doi.org/10.1007/s40314-023-02361-3

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