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Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations |
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| Authors: | Yin Yang Yanping Chen Yunqing Huang & Wei Yang |
| Abstract: | A Legendre-collocation method is proposed to solve the nonlinearVolterra integral equations of the second kind. We provide arigorous error analysis for the proposed method, which indicates thatthe numerical errors in $L^2$-norm and $L^infty$-norm will decayexponentially provided that the kernel function is sufficientlysmooth. Numerical results are presented, which confirm thetheoretical prediction of the exponential rate of convergence. |
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