Wei Yunxia, Chen Yanping, Shi Xiulian, Zhang Yuanyuan
College of Mathematic and Information Science, Shandong Institute of Business and Technology, Yantai, 264005 China.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631 China.
Springerplus. 2016 Oct 4;5(1):1710. doi: 10.1186/s40064-016-3358-z. eCollection 2016.
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] ( 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.
在本文中，我们给出了雅可比谱配置法用于逼近多维非线性沃尔泰拉积分方程解时的收敛性质。当源函数和核函数光滑时，解具有足够的光滑性。我们选择与多维雅可比权函数[公式：见原文]（表示空间维数）相关联的雅可比 - 高斯点作为配置点。在[公式：见原文]-范数和[公式：见原文]-范数下的误差分析从理论上证明了谱配置法在多维空间中的指数收敛性。我们给出两个数值例子以说明所提出的雅可比谱配置法的有效性。
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