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Symplectic‐preserving Fourier spectral scheme for space fractional Klein–Gordon–Schrödinger equations
Author(s) -
Wang Junjie
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22565
Subject(s) - mathematics , symplectic geometry , schrödinger equation , hamiltonian system , hamiltonian (control theory) , mathematical analysis , conservation law , fourier series , fourier transform , mathematical optimization
In the paper, the symplectic‐preserving Fourier spectral scheme is presented for space fractional Klein–Gordon–Schrödinger equations involving fractional Laplacian. First, we validate space fractional Klein–Gordon–Schrödinger equations that can be expressed as an infinite dimension Hamiltonian system. We apply the Fourier spectral method in space, and the semi‐discrete system preserves the mass and energy conservation laws. Second, by introducing some variables, the semi‐discrete system can be expressed as a large Hamiltonian ordinary differential system. We use the midpoint rule in time to semi‐discrete system, and obtain a symplectic approximation scheme of these equations. Moreover, we can prove that the scheme is convergent. To reduce the computational cost, we introduce the splitting idea for the symplectic integrators. Finally, we give numerical experiments to show the efficiency of the scheme.