中立型多延迟积分微分代数方程二步Runge-Kutta方法渐近稳定性(英文)  

Asymptotic stability of two-step Runge-Kuttamethods for systems of neutral multidelay-integro-differential-algebraic equations

作　　者：袁海燕[1] 宋成[2] 赵景军[3] 曲绍平[1] 

机构地区：[1]黑龙江工程学院数学系,哈尔滨150050 [2]哈尔滨商业大学管理学院,哈尔滨150028 [3]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2013年第2期187-194,共8页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundation the Eductation Department of Heilongjiang Province(12523039)

摘　　要：分析向量值形式的中立型多延迟积分微分代数方程二步Runge-Kutta方法的渐近稳定性。首先给出中立型多延迟积分微分代数方程解析解渐近稳定的定义,并给出使得解析解渐近稳定的充分条件。随后给出二步Runge-Kutta方法的一般形式和数值解渐近稳定的定义,给出数值方法渐近稳定的充分条件,最后证明A-稳定的二步Runge-Kutta方法求解中立型多延迟积分微分代数方程是渐近稳定的,并给出数值算例验证结论。The asymptotic stability of the two-step Runge-Kutta methods for systems of neutral multidelay-integro-differential-algebraie equations （NMDIDAEs） , which have different delays in the entries of the vector valued unknown functions, is investigated. Firstly, the asymptotically stable definition of the multidelay-integro-differential-algebraic equations is given, and then a sufficient condition for the asymp- totic stability is presented. Subsequently, the general form of the two-step Runge-Kutta method and the definition of asymptotic stability for the numerical solution are introduced. The sufficient conditions of as- ymptotical stability for the numerical method are given. Finally, it is proven that A-stable two-step Runge-Kutta methods are asymptotically stable for systems of neutral multidelay-integro-differential-algebraic equations. Numerical examples are given to verify the conclusions.

关 键 词：渐近稳定性 多延迟积分微分代数方程 二步Runge—Kutta方法 A-稳定 特征多项式 数值方法 

分 类 号：O189.1[理学—数学]