四阶Runge-Kutta格式及五阶Runge-Kutta格式的证明  

A Proof for the Fourth Order and Fifth Order of Runge-Kutta Forms

作　　者：郭菊喜 

机构地区：[1]岭南师范学院数学与计算科学学院,广东湛江524000

出　　处：《乐山师范学院学报》2016年第4期8-15,共8页Journal of Leshan Normal University

摘　　要：基于Taylor展开方法,在二阶和三阶Runge-Kutta格式的基础上证明了具有四阶精度的四阶Runge-Kutta格式所满足的条件,同时推导出了五阶Runge-Kutta格式,并证明了具有五阶精度的五阶Runge-Kutta格式所满足的条件。数值例子的计算结果表明五阶Runge-Kutta格式具有较高精度。Based upon the method of Taylor series expansion,the conditions which the forth order of Runge-Kutta form with fourth precision satisfies is proved upon the second and the third order of Runge-Kutta forms. At the same time,the fifth order of Runge-Kutta form is deduced,and it is also proved that the conditions which the fifth order of Runge-Kutta form with fifth precision satisfies. The calculating results of numerical examples show that the fifth order Runge-Kutta form is highly accurate.

关 键 词：TAYLOR展式 平均斜率 Runge-Kutta格式 

分 类 号：O241.8[理学—计算数学]