奇异延迟微分方程数值仿真的两步连续Runge-Kutta方法  

Two-Step Continuity Runge-Kutta Methods of Numerical Simulation for Singular Delay Differential Equations

作　　者：冷欣[1,2] 刘德贵[1,2] 宋晓秋[1] 陈丽容[1] 

机构地区：[1]北京计算机应用与仿真技术研究所 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《系统仿真学报》2005年第3期590-594,共5页Journal of System Simulation

摘　　要：提出在当前的积分步内计算级值时,放松延迟对计算的影响的思想,构造了一类奇异延迟微分方程数值仿真的两步连续 Runge-Kutta 方法(TSCRK),讨论了方法的构造,方法阶条件,证明了方法的收敛性,分析了方法的稳定性。这类方法具有优良的稳定性和较高的阶级,并保持了显式的求解过程。数值试验表明方法是有效的。In this paper, an idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods (TSCRK) of numerical simulation for singular delay differential equations are presented. The construction, order conditions and convergence of the methods are studied. Analysis of numerical stability of methods is given. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.

关 键 词：奇异延迟微分方程 两步连续Runge-Kutta方法 数值稳定性分析 收敛性 

分 类 号：O241.8[理学—计算数学]