Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels

Abstract

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.