Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation

We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi–Gauss points associated with the multidimensional Jacobi weight function [Formula: see text] (d denotes the space dimensions) as the collocation points. The error analysis in [Formula: see text] -norm and [Formula: see text] -norm theoretically justifies the exponential convergence of spectral collocation method in multidimensional space. We give two numerical examples in order to illustrate the validity of the proposed Jacobi spectral collocation method.