带线性延迟项的Volterra积分方程研究（英文）  

Studies on the Volterra Integral Equation with Linear Delay

作　　者：郑伟珊[1] ZHENG Wei-shan(Colloge 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,中国潮州521041

出　　处：《湖南师范大学自然科学学报》2017年第4期83-88,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11626074);韩山师范学院创新强校项目(Z16027);韩山师范学院扶持项目(201404);中山大学广东省计算科学重点实验室开放基金资助项目(2016011)

摘　　要：本文主要研究带线性延迟项的Volterra型积分方程收敛情况.首先通过线性变换,我们将原先定义在[0,T]区间上带线性延迟项的Volterra型积分方程转换成定义在固定区间[-1,1]上的方程,然后利用Gauss积分公式求得近似解,进而再利用Chebyshev谱配置方法分析该方程的收敛性,最终借助格朗沃不等式及相关引理分析获得方程在L~∞和L_(ω~c)~2范数意义下呈现指数收敛的结论.最后给出数值例子,验证理论证明的结论.This paper is concerned about the Volterra integral equation with linear delay.First we transfer the integral interval [0,T] into interval [-1, 1] through the conversion of variables.Then we use the Gauss quadrature formula to get the approximate solutions.After that the Chebyshev spectral-collocation method is proposed to solve the equation.With the help of Gronwall inequality and some other lemmas, a rigorous error analysis is provided for the proposed method, which shows that the numerical error decay exponentially in the innity norm and the Chebyshev weighted Hilbert space norms.In the end, numerical example is given to confirm the theoretical results.

关 键 词：Chebyshev谱配置方法 线性延迟项 VOLTERRA型积分方程 误差分析 

分 类 号：O242.2[理学—计算数学]