Multiderivative extended Runge-Kutta-Nystrom methods for multi-frequency oscillatory systems

作者：Zhao, Jingjun; Li, Yu; Xu, Yang^*

来源：International Journal of Computer Mathematics, 2018, 95(1): 231-254.

DOI：10.1080/00207160.2017.1366462

• Perturbed oscillatory systems
• Hamiltonian systems
• multiderivative extended Runge-Kutta-Nystrom methods
• order conditions
• phase properties

In this paper, a class of multistage and multivalue numerical methods called multiderivative extended Runge-Kutta-Nystrom (MERKN) methods are presented for the integration of multi-frequency oscillatory systems. The order conditions of these schemes are derived by using the theory of extended Nystrom trees and B-series. To simplify the construction of the new methods, the order conditions are simplified by omitting the redundant trees. Based on the simplified-order conditions, a family of three-stage and one-parameter explicit MERKN methods of order five is constructed. Meanwhile, the order of energy preservation, the stability and the phase properties of the new methods are analysed, and a three-stage method with minimal dispersion error is obtained. The results of numerical experiments demonstrate the efficiency of our new methods in comparison with some other RKN-type methods.

• 出版日期2018
• 单位哈尔滨工业大学; 黑龙江八一农垦大学