Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations (Advances in Applied Mathematics and Mechanics, 2018)
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 $L^∞$-norm will decayexponentially provided that the kernel function is sufficientlysmooth. Numerical results are presented, which confirm thetheoretical prediction of the exponential rate of convergence.