A spectral collocation method for multidimensional nonlinear weakly singular Volterra integral equation

被引：12
|
作者：
Wei, Yunxia [1 ]
Chen, Yanping [2 ]
Shi, Xiulian [3 ]
机构：
[1] Zhejiang Univ Water Resources & Elect Power, Hangzhou 310018, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[3] Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526061, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 331卷
基金：
中国国家自然科学基金;
关键词：
Multidimensional nonlinear Volterra integral equation; Chebyshev collocation discretization; Multidimensional Gauss quadrature formula; Convergence analysis; RUNGE-KUTTA METHODS; CONVERGENCE ANALYSIS; POLYNOMIAL-APPROXIMATION; ORDER;
D O I：
10.1016/j.cam.2017.09.037
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the convergence properties of Chebyshev spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation of the second kind with a weakly singular kernel. We consider the case that the underlying solution is sufficiently smooth. The Chebyshev collocation discretization is proposed for this equation. In the present paper, we provide a rigorous error analysis which justifies that the errors of approximate solution decay exponentially in weighted L-2 norm and L-infinity norm. Numerical results are presented to demonstrate the effectiveness of the spectral method. (C) 2017 Elsevier B.V. All rights reserved.
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页码：52 / 63
页数：12
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