二阶时滞Volterra微积分方程数值研究（英文）  

Numerical Analysis for Second Order Volterra Integro-Differential Equation with Vanishing Delay

作　　者：郑伟珊 ZHENG Weishan(College of Mathematics and Statistics,Hanshan Normal University,Chaozhou 521041,China)

机构地区：[1]韩山师范学院数学与统计学院,广东潮州521041

出　　处：《应用数学》2019年第1期141-152,共12页Mathematica Applicata

基　　金：Supported by the National Natural Scienie Foundation of China(11626074);Hanshan Normal University project(LF201404,216027,2017HJGJCJY009)

摘　　要：本文研究二阶时滞Volterra微积分方程收敛问题.利用勒让德谱方法,获得方程的精确解与近似解及精确导数与近似导数误差在指定范数空间呈指数收敛结果,推广了二阶Volterra方程的结果.In this paper, we use a Legendre-collocation spectral method to deal with the second order Volterra integro-differential equation, which contains vanishing delay.The convergence analysis for the proposed method is established in both L^2-norm and L^∞-norm. The goal is to provide a rigorous error analysis for the given equation. In the end of the paper, we give an example to confirm our deduce.

关 键 词：收敛分析 勒让德谱方法 二阶Volterra微积分方程 时滞 

分 类 号：O241[理学—计算数学]