Title :
New Runge-Kutta Methods with Improved Internal Orders
Author :
Zhang, Yonghui ; Liu, Zhongli ; Lei, Xiudong ; You, Xiong
Author_Institution :
Jiangsu Key Lab. for Inf. Agric., Nanjing Agric. Univ., Nanjing, China
Abstract :
In this paper the order conditions for Runge-Kutta (RK) methods are presented based on Butcher´s B-series theory. New concepts of internal orders vector and stage orders of RK methods are proposed. The internal and stage orders of some classical RK methods are examined. Two new methods with improved internal orders are constructed. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with the traditional RK methods.
Keywords :
Runge-Kutta methods; differential equations; initial value problems; Butcher B-series theory; Runge-Kutta method; initial value problem; internal orders vector; numerical experiment; stage orders; Accuracy; Differential equations; Equations; Hafnium; Mathematical model; Measurement uncertainty; Oscillators; Runge-Kutta method; error constant; internal order; order condition; stage order;
Conference_Titel :
Information and Computing (ICIC), 2011 Fourth International Conference on
Conference_Location :
Phuket Island
Print_ISBN :
978-1-61284-688-0
DOI :
10.1109/ICIC.2011.79
