| Oscillation of Numerical Solution in the Runge-Kutta Methods for Equation x＇（t） = ax（t） ＋ aox（[t]） |
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| 作者姓名： | Qi WANG ;Shen-shan QIU |
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| 作者单位： | [1]School of Apllied Mathematics, Guangdong University of Technology, Guangzhou 510006, China; [2]CSIB Software Technology Center; The Administrative Commission of Guangzhou Tianhe Software Park~Guangzhou 510635, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China(No.11201084);the State Scholarship Fund grant[2013]3018 from the China Scholarship Council |
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| 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.
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| 关 键 词： | 特征方程 数值解 AOX 振荡 塔 数值方法 数值试验 解析解 |
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