[1]舒?? 欣,李志林,游?? 雄,等.极小化误差常数的4 阶Runge- Kut ta 方法[J].常州大学学报(自然科学版),2009,(03):64-67.
　SHU Xin,LI Zhi- lin,YOU Xiong,et al.Fourth Order Runge- Kutta Method with Minimized Error Constant[J].Journal of Changzhou University(Natural Science Edition),2009,(03):64-67.
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极小化误差常数的4 阶Runge- Kut ta 方法()
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常州大学学报(自然科学版)[ISSN:2095-0411/CN:32-1822/N]

卷:
期数:
2009年03期
页码:
64-67
栏目:
数理科学
出版日期:
2009-09-25

文章信息/Info

Title:
Fourth Order Runge- Kutta Method with Minimized Error Constant
作者:
舒?? 欣1 ;  李志林2 ;  游?? 雄1;  3
1?南京农业大学应用数学系, 江苏南京210095; 2?江苏工业学院, 江苏 常州 213164; 3?南京大学数学系, 江苏南京210093
Author(s):
SHU Xin1 ;  LI Zhi- lin2 ;  YOU Xiong1;  3
1. Department of A pplied Mathemat ics, N anjing Agricultural University, Nanjing 210095, China; 2. Jiang su Polytechnic U niversity, Changzho u 213164, China; 3. Depar tment of Mathematics, Nanjing University, Nanjing 210093, China
关键词:
Runge- Kutt a 法;  阶条件;  误差常数;  极小化
Keywords:
Runge- Kutta methods;  order co nditions;  erro r constant ;  minimizat ion
分类号:
O 241. 81 ??
文献标志码:
A
摘要:
在But ch er 根树理论基础上引入Run ge- Kut t a 方法的阶条件, 并通过误差常数极小化技术得到一个新的4 阶方法。数值 实验结果表明, 新方法与现有文献中的几个高效方法相比, 在计算精度及效率上具有明显的优越性。
Abstract:
The order conditions for Rung e- Kutta methods are presented based on Butcher??s rooted t ree theory. A new Runge- Kut ta method is o btained by means of minimizing the error constant . The r esults of numerical experiments show the competence of the new method in accuracy and ef ficiency w hen they are compared w ith some hig hly ef ficient codes in the liter ature.

参考文献/References:

[1] But cher J C . Numeri cal m ethods f or ordinary di ff erent ial equat ion s [M] . Engl and: J ohn Wiley & S ons, 2003.
[2] H airer E, Nrs et t S P, Wanner G. Solving ordin ary dif f erent ial equat ions I, Nonst iff problems [M] . Berlin: Springer- Verlag, 1993.
[3] Goeken D, John son O. Fifth - ord er Runge- Kut t a with higher order derivat ive approximat ions [J] . Elect ronic Journ al of Dif f erent ial Equat ions, 1999, 2: 1- 9.
[4] Goek en D, John son O. Run ge- Kut t a with higher order derivat ive approximat ions [J] . Appl Num er Math, 2000, 34: 207 - 218.
[5] Podisuk M. Open form ula of Ru nge- Kut t a method f or sol vin g aut on om ous ordinary dif f erent ial equat ion [J] . Appli ed Mathematics and Comput at ion , 2006, 181: 536- 542.
[6] Wu X. A cl as s of Runge- Kut t a of order three and fou r with reduced evaluat ions of funct ion [J] . Appl Num er Math , 2003, 146: 417- 432.
[7] Vyver H V. A symplect ic Run ge- Ku tt a - Nys t r??Om method w ith m inimal ph as e- lag [J] . Ph ys L et t , 2007, 367: 16 - 24.
[8] Zingg D W, Chis holm T R. Run ge- Ku tt a methods f or linear ordinary dif f erent ial equ at ions [J] . Appl Numer Math , 1999, 31: 227- 238.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金项目资助( 10771099) 作者简介: 舒欣( 1984- ) , 男, 安徽绩溪人, 博士生; 通讯联系人: 游雄。
更新日期/Last Update: 2009-09-25