Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations

被引：34
|
作者：
Wei, Yunxia [2 ]
Chen, Yanping [1 ]
机构：
[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
来源：
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2011年 / 4卷 / 03期
基金：
美国国家科学基金会;
关键词：
Second order Volterra integro-differential equations; Gauss quadrature formula; Legendre-collocation methods; convergence analysis; DIFFERENTIAL-EQUATIONS; INTEGRAL-EQUATIONS; APPROXIMATIONS;
D O I：
10.4208/nmtma.2011.m1028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the L-infinity-norm and L-2-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.
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页码：419 / 438
页数：20
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