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A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors in $L^2$-norm and $L^\infty$-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m163}, url = {http://global-sci.org/intro/article_detail/aamm/10945.html} }A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors in $L^2$-norm and $L^\infty$-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.