Title :
An Optimized Fourth Order Runge-Kutta Method
Author :
You, Xiong ; Yao, Xinmeng ; Shu, Xin
Author_Institution :
Dept. of Appl. Math., Nanjing Agric. Univ., Nanjing, China
Abstract :
In this paper the order conditions for Runge-Kutta methods are presented based on Butcher´s rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.
Keywords :
Runge-Kutta methods; trees (mathematics); Butcher rooted tree theory; optimized fourth order Runge-Kutta method; order conditions; Books; Computer errors; Computer science; Differential equations; Finite wordlength effects; Mathematics; Minimization methods; Nonlinear equations; Optimization methods; Stability; Runge-Kutta method; error constant; minimization; order condition;
Conference_Titel :
Information and Computing (ICIC), 2010 Third International Conference on
Conference_Location :
Wuxi, Jiang Su
Print_ISBN :
978-1-4244-7081-5
Electronic_ISBN :
978-1-4244-7082-2
DOI :
10.1109/ICIC.2010.195
