一类组合两步连续RK-Rosenbrock方法  

A Class of Combined Two-Step Continuity RK-Rosenbrock Methods

作　　者：冷欣[1] 刘德贵[1] 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,北京100854

出　　处：《系统仿真学报》2007年第17期3945-3948,共4页Journal of System Simulation

摘　　要：对于一个大的刚性延迟微分方程系统,除了延迟分量给予系统影响外,还常常会出现系统的解分量有的变化很快,而有的变化很慢的情况。此时,可以把大的刚性延迟微分方程系统分解成为两个耦合的子系统,一个是描述系统快变部分的刚性延迟子系统,另一个是描述系统慢变部分的非刚性延迟子系统。对于分解的刚性延迟微分方程大系统,构造了一类用于求解刚性延迟微分方程的组合两步连续RK-Rosenbrock方法,讨论了方法的构造,方法的阶条件,证明了方法的收敛性,分析了方法的稳定性,数值试验表明方法是有效的。Some solution of stiff delay differential equations change fast and others change slowly. The system could be partitioned into two coupling subsystems, one for stiff delay differential equations and the other for non-stiff delay differential equations. A class of combined two-step continuity RK-Rosenbrock methods was constructed for solving stiff singular and stiff nonsingular delay differential equations respectively toward a partitioned system of stiff delay differential equations. Two-step Runge-Kutta methods were used for solving nonstiff delay subsystem and two-step Rosenbrock methods were used for solving stiff delay subsystem. The construction, order conditions, numerical stability and convergence of the methods were studied. Numerical experiments show that the methods are efficient,

关 键 词：刚性延迟微分方程 两步连续RK-Rosenbrock方法 数值稳定性分析 收敛性 

分 类 号：O241.81[理学—计算数学]