Abstract:

In the paper, the symplectic-preserving schemes are presented for fractional Klein-Gordon-Schrödinger equations. First, we give the infinite-dimensional Hamilton with fractional Laplacian operator and conservation laws, and change the above quantum mechanical equations into Hamilton system. We apply the central finite difference schemes to discrete Klein-Gordon-Schrödinger in space, and yield a large Hamilton ordinary differential system. Second, we use the midpoint rule in time to Hamiltonian ordinary differential system, and obtain a symplectic approximation of the these equations. Moreover, we analyze the conservation of the numerical scheme. Finally, we give numerical experiments to show the verify the efficiency of the conservative finite difference scheme.

Key words: Fractional Klein-Gordon-Schrödinger equations, Conservative scheme, Symplectic scheme, Convergence