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A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind

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Abstract

The subject of the present paper is to apply the Jacobi spectral collocation method for multidimensional linear Volterra integral equation with a weakly singular kernel. Here, we assume that the solution is sufficiently smooth. An error analysis has been provided which justifies that the approximate solution converges exponentially to the exact solution. Finally, two numerical examples are given to clarify the efficiency and accuracy of the method.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (11671157) and Shandong Province Natural Science Foundation of China (ZR2017MA005).

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Authors and Affiliations

  1. Zhejiang University of Water Resources and Electric Power, Hangzhou, 310018, China

    Yunxia Wei

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yanping Chen

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  1. Yunxia Wei
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  2. Yanping Chen
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Correspondence to Yanping Chen.

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Wei, Y., Chen, Y. A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind. J Sci Comput 79, 1801–1813 (2019). https://doi.org/10.1007/s10915-019-00912-7

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  • DOI: https://doi.org/10.1007/s10915-019-00912-7

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