Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation

doi:10.1088/1674-1056/28/5/050201

中国物理B ›› 2019, Vol. 28 ›› Issue (5): 50201-050201.doi: 10.1088/1674-1056/28/5/050201

• GENERAL • 下一篇

Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation

Feng Guo(郭峰)

Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

收稿日期:2019-01-14 修回日期:2019-03-07 出版日期:2019-05-05 发布日期:2019-05-05
通讯作者: Feng Guo E-mail:hydhgf@163.com
基金资助:
Project supported by the Program for Innovative Research Team in Science and Technology in Fujian Province University, China, the Quanzhou High Level Talents Support Plan, China (Grant No. 2017ZT012), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University, China (Grant No. ZQN-YX502).

Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation

Feng Guo(郭峰)

Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received:2019-01-14 Revised:2019-03-07 Online:2019-05-05 Published:2019-05-05
Contact: Feng Guo E-mail:hydhgf@163.com
Supported by:
Project supported by the Program for Innovative Research Team in Science and Technology in Fujian Province University, China, the Quanzhou High Level Talents Support Plan, China (Grant No. 2017ZT012), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University, China (Grant No. ZQN-YX502).

摘要/Abstract

摘要： A conformal multi-symplectic method has been proposed for the damped Korteweg-de Vries (DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme, we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations (PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.

关键词: conformal multi-symplectic method, damped Korteweg-de Vries (KdV) equation, dissipation preservation

Abstract: A conformal multi-symplectic method has been proposed for the damped Korteweg-de Vries (DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme, we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations (PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.

Key words: conformal multi-symplectic method, damped Korteweg-de Vries (KdV) equation, dissipation preservation

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

02.70.Bf (Finite-difference methods) 02.60.Cb (Numerical simulation; solution of equations)

郭峰. Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation[J]. 中国物理B, 2019, 28(5): 50201-050201.

Feng Guo(郭峰). Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation[J]. Chin. Phys. B, 2019, 28(5): 50201-050201.

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Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation

Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation

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