A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel  

作　　者：Yunxia Wei Yanping Chen 

机构地区：[1]College of Mathematic and Information Science,Shandong Institute of Business and Technology,Yantai 264005,Shandong,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,Guangdong,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2013年第2期424-446,共23页高等学校计算数学学报（英文版）

基　　金：supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008);National Science Foundation of China(10971074);Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009).

摘　　要：This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation with a weakly singular kernel.The solution of this equation,even for analytic data,is not smooth on the entire interval of integration.The Jacobi collocation discretization is proposed for the given equation.A rigorous analysis of error bound is also provided which theoretically justifies that both the error of approximate solution and the error of approximate derivative of the solution decay exponentially in L∞norm and weighted L2 norm.Numerical results are presented to demonstrate the effectiveness of the spectral method.

关 键 词：Neutral Volterra integro-differential equation weakly singular kernel Jacobi collocation discretization convergence analysis 

分 类 号：O17[理学—数学]