Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

Abstract

AbstractA 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 indicate that the numerical errors inL2-norm andL∞-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.