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Spectral collocation method for system of weakly singular Volterra integral equations

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Abstract

Based on our previous research, we investigate spectral collocation method for system of weakly singular Volterra integral equations. The provided convergence analysis shows that global convergence order is related to regularity of the solution to this system, and the local convergence order on collocation points only depends on the regularity of kernel functions. Numerical experiments are carried out to confirm these theoretical results. Numerical methods are developed to solve nonlinear system of weakly singular Volterra integral equations and high-order weakly singular Volterra integro-differential equations.

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Funding

This work is supported by the Natural Science Foundation of Guangdong Province of China (2017A030310636, 2018A030313236), the Opening Project of Guangdong High Performance Computing Society (2017060104), and the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (2016001).

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  1. School of Financial Mathematics and Statistic, Guangdong University of Finance, Guangzhou, 510521, China

    Zhendong Gu

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  1. Zhendong Gu
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Correspondence to Zhendong Gu.

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Communicated by: Jan Hesthaven

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Gu, Z. Spectral collocation method for system of weakly singular Volterra integral equations. Adv Comput Math 45, 2677–2699 (2019). https://doi.org/10.1007/s10444-019-09703-y

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  • DOI: https://doi.org/10.1007/s10444-019-09703-y

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