title: Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation.
abstract: 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] (ddenotes 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.
authors: College of Mathematic and Information Science, Shandong Institute of Business and Technology, Yantai, 264005 China.
authors: Yunxia
authors: Y
authors: Wei
authors: School of Mathematical Sciences, South China Normal University, Guangzhou, 510631 China.
authors: Yanping
authors: Y
authors: Chen
authors: School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, 526061 China.
authors: Xiulian
authors: X
authors: Shi
authors: Department of Mathematics and Information Science, Yantai University, Yantai, 264005 China.
authors: Yuanyuan
authors: Y
authors: Zhang
keywords: Error estimates; Jacobi collocation discretization; Multidimensional Gauss quadrature formula; Multidimensional nonlinear Volterra integral equation