叠加Runge-Kutta方法的几类稳定性分析  

Some stability properties of additive Runge-Kutta methods

作　　者：袁海燕[1,2] 赵爽[1] 

机构地区：[1]黑龙江工程学院数学系,黑龙江哈尔滨150050 [2]哈尔滨工业大学,黑龙江哈尔滨150001

出　　处：《黑龙江工程学院学报》2011年第1期75-77,共3页Journal of Heilongjiang Institute of Technology

摘　　要：数值积分处理非线性刚性初值问题时,常常要求数值方法的BN-稳定性。在许多应用中,由于定义模块的微分算子的特殊结构,使得用叠加方法数值处理很方便。给出叠加Runge-Kutta方法的BN-稳定的一个充要条件及它的代数稳定性和AN-稳定性的定义,同时给出这几类稳定性的等价条件。An important requirement of numerical methods for the integration of nonlinear stiff initial value problems is BN-stability.In many applications it is also convenient to use additive methods to take advantage of the special structure of the differential operator that defines the model.The purpose of this paper is to provide a necessary and sufficient condition for the BN-stability of additive Runge-Kutta methods,introduce the algebraic stability and AN-stability and prove they are equivalent.

关 键 词：BN-稳定 AN-稳定 代数稳定 叠加Runge-Kutta方法 

分 类 号：TP751.1[自动化与计算机技术—检测技术与自动化装置]