Abstract
We investigate Chebyshev spectral collocation method for system of nonlinear Volterra integral equations. We choose Chebyshev Gauss points as collocation points, and approximate integral terms by Legendre Gauss quadrature formula. The provided convergence analysis shows that numerical errors decay exponentially, which is one of the most prominent features of spectral methods. Numerical experiments are carried out to confirm theoretical results. We have never seen any paper investigating the spectral method for the system of nonlinear Volterra integral equations (VIEs). The present method and corresponding convergence analysis would be useful in studying numerical methods for the system of integral equations and partial differential equations.
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Funding
This work is supported by 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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Gu, Z. Chebyshev spectral collocation method for system of nonlinear Volterra integral equations. Numer Algor 83, 243–263 (2020). https://doi.org/10.1007/s11075-019-00679-w
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DOI: https://doi.org/10.1007/s11075-019-00679-w