The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:353

Article

Li, Jiyong^1,2  Shi, Wei³  Wu, Xinyuan^4,5 

[1] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Hebei Key Lab Computat Math & Applicat, Shijiazhuang 050024, Hebei, Peoples R China

[3] Nanjing Tech Univ, Coll Math Sci, Nanjing 211816, Jiangsu, Peoples R China

[4] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China

[5] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

关键词: Adapted Runge-Kutta-Nystrom methods;    Oscillatory problems;    Hamiltonian systems;    Symplectic conditions;    Main frequency;   

DOI  :  10.1016/j.cam.2018.12.026

来源: Elsevier

【 摘 要 】

Adapted Runge-Kutta-Nystrom (ARKN) methods for solving the oscillatory problem q ''(t)+w(2)q(t) = f(q(t)) have been investigated by several authors. Recently, Shi et al. [Comput. Phys. Comm. 183 (2012) 1250-1258] conclude that there exist only one-stage explicit symplectic ARKN methods and the algebraic order cannot exceed two. In this paper we investigate the symplecticity of ARKN methods and present that there exist explicit symplectic ARKN methods with several stages and algebraic order greater than two. Some numerical experiments are provided to confirm the theoretical expectations. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free