Abstract
The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L 2 norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical examples are given to illustrate the theoretical results.
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Wan, Z., Chen, Y. & Huang, Y. Legendre spectral Galerkin method for second-kind Volterra integral equations. Front. Math. China 4, 181–193 (2009). https://doi.org/10.1007/s11464-009-0002-z
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DOI: https://doi.org/10.1007/s11464-009-0002-z