TY - JOUR
T1 - A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation
AU - Yang , Yanhong
AU - Song , Yongzhong
AU - Li , Haochen
AU - Wang , Yushun
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 242
EP - 260
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2017-0038
UR - https://global-sci.org/intro/article_detail/aamm/10509.html
KW - Klein-Gordon-Schrödinger equation, Fourier pseudospectral method, symplectic scheme, explicit scheme.
AB - <p style="text-align: justify;">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
is generally implicit or semi-implicit. Linear stability analysis is carried out 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.</p>