On fifth order Runge-Kutta methods
On fifth order Runge-Kutta methods
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关于五阶龙格-库塔方法
DOI：
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发表时间：
1995
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通讯作者：
J. Butcher
中科院分区：
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作者：
J. Butcher
给出了一种6阶龙格-库塔法，它在求解标量微分方程组时阶数为5，而在求解一般微分方程组时仅为4阶。这种方法的存在强调了在向量值环境中进行理论分析的必要性，而不是像库塔和一些较新的作者所做的那样在一维环境中进行理论分析。
A 6 stage Runge-Kutta method is derived with the property that its order is 5 when used to solve a scalar differential equation but only 4 when used to solve a general system of differential equations. The existence of such a method underlines the necessity of carrying out theoretical analyses in a vector valued setting rather than in a one-dimensional setting as in the work of Kutta and some more recent authors.