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

被引：35

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.

引用

页码：419 / 438

页数：20

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