Abstract
We apply Jacobi spectral collocation approximation to a two-dimensional nonlinear weakly singular Volterra integral equation with smooth solutions. Under reasonable assumptions on the nonlinearity, we carry out complete convergence analysis of the numerical approximation in the L∞-norm and weighted L2-norm. The provided numerical examples show that the proposed spectral method enjoys spectral accuracy.
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* This work is supported by National Science Foundation of China (11501499, 11401347).
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Shi, X., Wei, Y. Convergence analysis of the spectral collocation methods for two-dimensional nonlinear weakly singular Volterra integral equations*. Lith Math J 58, 75–94 (2018). https://doi.org/10.1007/s10986-018-9387-2
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DOI: https://doi.org/10.1007/s10986-018-9387-2