A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrodinger Equation  

作　　者：Yanhong Yang Yongzhong Song Haochen Li Yushun Wang 

机构地区：[1]Jiangsu Key Laboratory for NSLSCS,Institute of Mathematics,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China [2]Department of Mathematics,College of Taizhou,Nanjing Normal University,Taizhou 225300,China [3]LMAM,CAPT and School of Mathematical Sciences,PekingUniversity,Beijing 100871,China

出　　处：《Advances in Applied Mathematics and Mechanics》2018年第1期242-260,共19页应用数学与力学进展（英文）

基　　金：This work is supported by the Jiangsu Collaborative Innovation Center for Climate Change,the National Natural Science Foundation of China(Grant Nos.11271195 and 11271196)and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

摘　　要：In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger equation.The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in time.After composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space,we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in time.The canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be symplectic.The new scheme is totally explicitwhereas symplectic scheme are generally implicit or semi-implicit.Linear stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is given.The numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.

关 键 词：Klein-Gordon-Schr odinger equation Fourier pseudospectral method symplectic scheme explicit scheme 

分 类 号：O17[理学—数学]