A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrödinger Equation (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we propose an explicit symplectic Fourier pseudospectralmethod for solving the Klein-Gordon-Schrödinger equation. The key idea is to rewritethe equation as an infinite-dimensional Hamiltonian system and discrete the systemby using Fourier pseudospectral method in space and symplectic Euler method intime. After composing two different symplectic Euler methods for the ODEs resultedfrom semi-discretization in space, we get a new explicit scheme for the target equationwhich is of second order in space and spectral accuracy in time. The canonical Hamiltonianform of the resulted ODEs is presented and the new derived scheme is provedstrictly to be symplectic. The new scheme is totally explicit whereas symplectic schemeis generally implicit or semi-implicit. Linear stability analysis is carried out and a necessaryCourant-Friedrichs-Lewy condition is given. The numerical results are reportedto test the accuracy and efficiency of the proposed method in long-term computing.