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

作　　者：Feng Guo 郭峰(Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University)

机构地区：[1]Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University

出　　处：《Chinese Physics B》2019年第5期20-26,共7页中国物理B（英文版）

基　　金：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);the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University,China(Grant No.ZQN-YX502)

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.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 

分 类 号：O175.29[理学—数学]