Volume 10, Issue 1
A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation

Yanhong Yang, Yongzhong Song, Haochen Li & Yushun Wang

Adv. Appl. Math. Mech., 10 (2018), pp. 242-260.

Published online: 2018-10

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  • Abstract

In this paper, we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schrödinger 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 explicit whereas 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

  • Keywords

Klein-Gordon-Schrödinger equation, Fourier pseudospectral method, symplectic scheme, explicit scheme.

  • AMS Subject Headings

65M70, 65M12, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-242, author = {}, title = {A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {242--260}, abstract = {

In this paper, we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schrödinger 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 explicit whereas 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

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0038}, url = {http://global-sci.org/intro/article_detail/aamm/10509.html} }
TY - JOUR T1 - A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 242 EP - 260 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0038 UR - https://global-sci.org/intro/aamm/10509.html KW - Klein-Gordon-Schrödinger equation, Fourier pseudospectral method, symplectic scheme, explicit scheme. AB -

In this paper, we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schrödinger 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 explicit whereas 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

Yanhong Yang, Yongzhong Song, Haochen Li & Yushun Wang. (2020). A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation. Advances in Applied Mathematics and Mechanics. 10 (1). 242-260. doi:10.4208/aamm.OA-2017-0038
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