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.

引用

页码：52 / 63

页数：12

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