| 具极小化局部截断误差的Runge-Kutta方法 |
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| 引用本文： | 张建国.具极小化局部截断误差的Runge-Kutta方法[J].四川师范大学学报(自然科学版),1990(4). |
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| 作者姓名： | 张建国 |
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| 作者单位： | 四川师范大学数学系 |
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| 基金项目： | 四川师范大学科研基金资助 |
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| 摘 要： | 使用本文提出的既不增加函数f(x,y)求值的个数计算又不要求f(x,y)及(?)~(i+j)f/(?)x~i(?)y~j 为有界的方法,便建立了具极小化局部截断误差的二级二阶直到四级四阶的Runge-Kutta 公式.这些公式均可用于求解非线性一阶常微分方程组,且是对Lotkin(1951)、Ralston(1962)、Merson(1975)、Scraton(1964)、England(1969)的结果的一种改善和推广.此外,当常微分方程组退化成一个方程时,Lotkin(1951)和Ralston(1962)的若于结果就是本文特例.
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| 关 键 词： | 局部截断误差 内积 Kronecker 积 范数 Taylot 展式 极小值 解曲线 |
RUNGE-KUTTA METHODS WITH MINIMIZING THE LOCAL TRUNCATION ERROR |
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| Zhang Jianguo.RUNGE-KUTTA METHODS WITH MINIMIZING THE LOCAL TRUNCATION ERROR[J].Journal of Sichuan Normal University(Natural Science),1990(4). |
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| Authors: | Zhang Jianguo |
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| Institution: | Department of Mathematics |
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| Abstract: | Using the method originated by author in this paper,which is a method with neither increasing additional evaluationof function f(x,y)nor requiring bounded condition for f(x,y)and((?)~(i+j)f)/((?)x~i(?)y~j),2-stage second-order up to 4-stage fourth-orderRunge-Kutta formulas with minimizing the local truncation error are established.These formulas can be applied to non-linear systems of first-order ordinary differential equation,and are the improvement and extension of the results that aredue to Lotkin(1951),Ralston(1962),Merson(1957),Scraton(1964)mad England(1969).Moreover,when a sysytem isdegenerated into a single differential equation,Lotkin's(1951)and Ralston's(1964)some important results are the specialcases of this paper. |
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| Keywords: | local truncation error inner product Kronecker product norm Taylor expansion minimal value solution curve |
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