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

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