Oscillation of Numerical Solution in the Runge-Kutta Methods for Equation x'(t)=ax(t)+a_0x([t])  

作　　者：Qi WANG Shen-shan QIU 

机构地区：[1]School of Apllied Mathematics,Guangdong University of Technology [2]CSIB Software Technology Center,The Administrative Commission of Guangzhou Tianhe Software Park

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第4期943-950,共8页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11201084);the State Scholarship Fund grant[2013]3018 from the China Scholarship Council

摘　　要：The paper de ls with oscillation of Runge-Kutta methods for equation x＇（t） = ax（t） ＋ aox（[t]）. The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given.The paper de ls with oscillation of Runge-Kutta methods for equation x＇（t） = ax（t） ＋ aox（[t]）. The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given.

关 键 词：piecewise continuous arguments Runge-Kutta methods stablity OSCILLATION 

分 类 号：O175[理学—数学]