Abstract:
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In this talk, we mainly introduce the symplectic scheme for the 1D space fractional Schr?dinger equation (SFSE). First, the symplectic conservation law is investigated for space semi-discretization systems of the SFSE based on the existing second-order central difference scheme and the existing fourth-order compact scheme. Then, the fourth-order central difference scheme of the fractional Laplacian is developed, and the resulting space semi-discretization system is shown to be a finite dimension Hamiltonian system of ordinary differential equations. Moreover, we get the full discretization scheme by applying the symplectic midpoint scheme to the Hamiltonian system. In particular, the space semi-discretization and the full discretization are shown to preserve some properties of the SFSE. Moreover, we introduce simply the symplectic-preserving Fourier spectral scheme for multi-dimensional space fractional Klein-Gordon-Schrodinger equations.
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