THE LONG TIME BEHAVIOR OF A SPECTRAL COLLOCATION METHOD FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

被引：3
|
作者：
Tang, Jie [1 ]
Xie, Ziqing [2 ]
Zhang, Zhimin [3 ,4 ]
机构：
[1] Hunan Univ Technol, Coll Sci, Zhuzhou 412007, Hunan, Peoples R China
[2] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
[3] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
[4] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2013年 / 18卷 / 03期
基金：
美国国家科学基金会;
关键词：
Pantograph delay differential equations; spectral collocation method; exponential convergence; domain decomposition; vanishing proportional delay; INTEGRAL-EQUATIONS; GALERKIN METHODS; SUPERCONVERGENCE;
D O I：
10.3934/dcdsb.2013.18.797
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose an efficient numerical method for delay differential equations with vanishing proportional delay qt (0 < q < 1). The algorithm is a mixture of the Legendre-Gauss collocation method and domain decomposition. It has global convergence and spectral accuracy provided that the data in the given pantograph delay differential equation are sufficiently smooth. Numerical results demonstrate the spectral accuracy of this approach and coincide well with theoretical analysis.
引用
收藏
页码：797 / 819
页数：23
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