Convergence analysis of spectral methods for high-order nonlinear Volterra integro-differential equations

被引:0
作者
Xiulian Shi
Fenglin Huang
Hanzhang Hu
机构
[1] Zhaoqing University,School of Mathematics and Statistics
[2] Xinyang Normal University,School of Mathematics and Statistics
[3] Jiaying University,School of Mathematics
来源
Computational and Applied Mathematics | 2019年 / 38卷
关键词
High-order Volterra integro-differential equations; Spectral methods; Convergence analysis; 65R20; 65M70; 45D05;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we propose and analyze Chebyshev spectral collocation approximation for high-order nonlinear Volterra integro-differential equations. Under reasonable assumptions on the nonlinearity, it is shown that this numerical method converges exponentially in both L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^\infty $$\end{document}-norm and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-norm. Numerical results of several test examples are presented and comparisons are made with some existing numerical methods to prove the superiority and the effectiveness of the proposed method.
引用
收藏
相关论文
共 74 条
[1]  
Aguilar M(1988)Collocation methods for second-order Volterra integro-differential equations Appl Numer Math 4 455-470
[2]  
Brunner H(2010)Convergence analysis of spectral methods for integro-differential equations with vanishing proportional delays J Comput Math 28 962-973
[3]  
Ali I(2016)A Legendre–Galerkin method for solving general Volterra functional integral equations Numer Algorithm 73 1159-1180
[4]  
Cai H(2009)Spectral methods for weakly singular Volterra integral equations with smooth solutions J Comput Appl Math 233 938-950
[5]  
Qi J(2010)Convergence analysis of Jacobi spectral collocation methods for Volterra integral equations with a weakly singular kernel Math Comput 79 147-167
[6]  
Chen Y(2013)A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions J Comput Math 31 47-56
[7]  
Tang T(2016)A spectral collocation method for a weakly singular Volterra integral equation of the second kind Adv Comput Math 42 1015-1030
[8]  
Chen Y(2009)On spectral methods for Volterra-type integro-differential equations J Comput Appl Math 230 333-340
[9]  
Tang T(2012)Convergence analysis of Jacobi spectral collocations methods for Alber-Volterra integral equations of second kind Front Math China 7 69-84
[10]  
Chen Y(2016)Numerical solutions for weakly singular Volterra integral equations using Chebyshev and Legendre pseudo-spectral Galerkin methods J Sci Comput 67 43-64