Legendre Spectral Collocation Methods for Pantograph Volterra Delay-Integro-Differential Equations

被引：61

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：

JOURNAL OF SCIENTIFIC COMPUTING | 2012年 / 53卷 / 03期

基金：

美国国家科学基金会;

关键词：

Volterra delay-integro-differential equations; Legendre-collocation methods; Gauss quadrature formula; Convergence analysis; RUNGE-KUTTA METHODS; INTEGRODIFFERENTIAL EQUATIONS; STABILITY ANALYSIS; CONVERGENCE;

D O I：

10.1007/s10915-012-9595-6

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 the Legendre spectral collocation methods when used to approximate smooth solutions of Volterra integro-differential equations with proportional (vanishing) delays. We provide a vigorous error analysis for the proposed methods. Furthermore, we prove that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L (2)-norm and L (a)-norm. Some numerical experiments are given to confirm the theoretical results.

引用

页码：672 / 688

页数：17

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