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解一类高阶变系数时滞微分系统的新型算法

发表时间:2009-07-15  浏览量:1612  下载量:648
全部作者: 吴树荣,张国凤,丁恒飞
作者单位: 兰州大学数学与统计学院
摘 要: 利用Chebyshev多项式与Taylor多项式相组合的方法,提出了一种求解高阶变系数时滞微分系统的新型数值算法。其构造思想是利用Chebyshev级数与Taylor级数逼近,把微分方程系统近似转化为矩阵方程系统,并利用Chebyshev配置方法,得到一个与原微分系统相关的关于Chebyshev系数的线性代数方程系统。最后通过一些数值例子验证了新算法的有效性。
关 键 词: 常微分方程;Chebyshev多项式;Taylor多项式;Chebyshev配置方法;时滞微分系统
Title: A new method for solving high-order linear delay Fredholm-Volterra integro-differential equations with variable cofficients
Author: WU Shurong, ZHANG Guofeng, DING Hengfei
Organization: School of Mathematics and Statistics, Lanzhou University
Abstract: In this paper, by means of the matrix relation between the Taylor and Chebyshev polynomials, the mentioned methods above are modified and developed in order to solve the systems of higher-order delay differential equations. This method transforms the integro-differential equations (IDE) system and the given conditions into the matrix equations by using the Chebyshev collocation method. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. In addition, examples are presented to illustrate the pertinent features of the method and the results are discussed.
Key words: ordinary differential equations; Chebyshev polynomials; Taylor polynomials; Chebyshev collocation method; delay differential system
发表期数: 2009年7月第13期
引用格式: 吴树荣,张国凤,丁恒飞. 解一类高阶变系数时滞微分系统的新型算法[J]. 中国科技论文在线精品论文,2009,2(13):1322-1328.
 
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