中国物理B ›› 2017, Vol. 26 ›› Issue (10): 100202-100202.doi: 10.1088/1674-1056/26/10/100202

• GENERAL • 上一篇    下一篇

Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity

Jia-Xiang Cai(蔡加祥), Qi Hong(洪旗), Bin Yang(杨斌)   

  1. 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;
    2. Graduate School of China Academy of Engineering Physics, Beijing 100083, China
  • 收稿日期:2017-04-08 修回日期:2017-06-13 出版日期:2017-10-05 发布日期:2017-10-05
  • 通讯作者: Jia-Xiang Cai E-mail:cjx1981@hytc.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 61672013) and the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems (Grant No. 201606).

Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity

Jia-Xiang Cai(蔡加祥)1, Qi Hong(洪旗)2, Bin Yang(杨斌)1   

  1. 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;
    2. Graduate School of China Academy of Engineering Physics, Beijing 100083, China
  • Received:2017-04-08 Revised:2017-06-13 Online:2017-10-05 Published:2017-10-05
  • Contact: Jia-Xiang Cai E-mail:cjx1981@hytc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 61672013) and the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems (Grant No. 201606).

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摘要： Local structure-preserving algorithms including multi-symplectic, local energy-and momentum-preserving schemes are proposed for the generalized Rosenau-RLW-KdV equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time-space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.

关键词: Rosenau-type equation, multi-symplectic conservation law, energy conservation law, structure-preserving algorithm

Abstract: Local structure-preserving algorithms including multi-symplectic, local energy-and momentum-preserving schemes are proposed for the generalized Rosenau-RLW-KdV equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time-space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.

Key words: Rosenau-type equation, multi-symplectic conservation law, energy conservation law, structure-preserving algorithm

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.70.Bf (Finite-difference methods) 02.70.Jn (Collocation methods) 02.70.Hm (Spectral methods)