超前型自变量分段连续型微分方程的Runge-Kutta方法的数值稳定性  

Numercial stability of Runge-Kutta methods for differential equation with piecewise continuous arguments of advanced type

作　　者：吕万金[1] 宋迎春[2] 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080 [2]哈尔滨理工大学应用科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2010年第3期281-286,共6页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究项目(11541269)

摘　　要：讨论一类特殊类型的超前型自变量分段连续型微分方程的解析解的稳定性,及应用Runge-Kutta方法于该方程所得数值解的稳定性。应用M.Z.Liu等在1990年证明的结果给出了N>2时解析解渐近稳定的充分条件;同时给出了N=2时解析解渐近稳定的充要条件。利用Or-der-Star和Padé逼近理论,给出了当Runge-Kutta方法的稳定函数是ex的Padé逼近时数值解保持解析解渐近稳定的充分必要条件。The stability of analytic solutions to a class of advanced and piecewise continuous differential equations and the stability of Runge-Kutta methods applying to this kind of equations are investigated. Applying the result given by M. Z. Liu in 1990, sufficient conditions under which the analytic solutions to the advanced differential equations are asymptotically stable are given. For N = 2, a necessary and sufficient condition under which the analytic solutions are asymptotically stable is obtained. From Order Star and Pad approximation, sufficient and necessary conditions under which the numerical solutions preserve the stability of the analytic solutions are given when the stability function of the Runge-Kutta method is the （r,s） -Pad6 approximation to ex.

关 键 词：分段连续 超前型 RUNGE-KUTTA方法 稳定性 

分 类 号：O189.1[理学—数学]