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

作　　者：Yunxia Wei Yanping Chen 

机构地区：[1]School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou 510275,China. [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2011年第3期419-438,共20页高等学校计算数学学报（英文版）

基　　金：the Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008),National Science Foundation of China(10971074).

摘　　要：A class of numerical methods is developed for second order Volterra integrodifferential 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∞-norm and L2-norm.Numerical examples illustrate the convergence and effectiveness of the numerical methods.

关 键 词：Second order Volterra integro-differential equations Gauss quadrature formula Legendre-collocation methods convergence analysis. 

分 类 号：O17[理学—数学]