带线性与非线性延迟项的Volterra积分方程研究  

The Volterra Integral Equation with Linear Delay and Nonlinear Delay

作　　者：郑伟珊[1] ZHENG Wei-shan(Colloge of Mathematics and Statistic,Hanshan Normal University,Chaozhou,Guangdong, 521041)

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：《韩山师范学院学报》2017年第3期15-22,共8页Journal of Hanshan Normal University

基　　金：中山大学广东省计算科学重点实验室开放基金项目(项目编号:2016011);韩山师范学院扶持项目(项目编号:201404);韩山师范学院创新强校项目(项目编号:Z16027)

摘　　要：主要研究了一类带线性延迟项与非线性延迟项Volterra型积分方程的收敛情况.首先通过线性变换,将原先定义在[0,T]区间上的带线性与非线性延迟项的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L2ωC范数意义下呈现指数收敛的结论,最后给出数值例子,算出误差估计并绘图展示,藉此验证理论证明的结论.This paper is a study of the Volterra integral equation with linear vanishing delay and nonlinear vanishing delay.First,transfer the integral interval[0,T]into interval[-1,1]through the conversion of variables.Then,use the Gauss quadrature formula to get the approximate solutions.Next,propose the Chebyshevspectralcollocation method 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 infinity norm and the Chebyshev weighted Hilbert space norms.In the end,numerical example is given to confirm the theoretical result.

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

分 类 号：O242.2[理学—计算数学]