| 数值方法中 Runge-Kutta 方法改进的探讨 |
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| 引用本文： | 赵学杰.数值方法中 Runge-Kutta 方法改进的探讨[J].衡水学院学报,2014(4):23-26. |
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| 作者姓名： | 赵学杰 |
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| 作者单位： | 德州学院数学科学学院,山东德州253023 |
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| 基金项目： | 山东省自然科学基金项目（ZR2010A1019）;山东省优秀中青年科学家科研奖励基金项目（BS2013HZ026） |
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| 摘 要： | 根据一阶常微分方程数值解的收敛性与稳定性，从固步长的Runge-Kutta法出发，考虑变步长的Runge-Kutta法，讨论了3种改进算法，即折半步长Runge．Kutta法、Runge-Kutta-Fehlberg法和Zadunaisky方法．并且分别讨论了3种变步长的Runge-Kutta法的精度及效率．
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| 关 键 词： | 数值解 Runge-Kutta法 变步长的Runge-Kutta法 自适应 |
Discussion on Improving Runge-Kutta Methods in Numerical Analysis |
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| ZHAO Xue-jie.Discussion on Improving Runge-Kutta Methods in Numerical Analysis[J].Journal of Hengshui University,2014(4):23-26. |
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| Authors: | ZHAO Xue-jie |
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| Institution: | ZHAO Xue-jie (School of Mathematical Sciences, Dezhou University, Dezhou, Shandong 253023, China) |
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| Abstract: | Based on the convergence and stability of the numerical solution of a differential equation, from a solid step Runge-Kutta method, it has considered variable step Runge-Kutta method. Three modified algorithm are discussed. They are step reduced by halfRunge-Kutta method, Runge-Kutta-Fehlberg method and Zadunaisky method. At the same time, the accuracy and efficiency of variable step Runge-Kutta method are discussed. |
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| Keywords: | numerical solution Runge-Kutta Method variable step Runge-Kutta method self-adaption |
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