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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

肖爱国 教授,湘潭大学数学与计算科学学院

Inviter: 唐贻发 研究员
Title:
Symplectic schemes for Schrodinger and Klein-Gordon-Schrodinger equations with fractional Laplacian
Time & Venue:
2021.10.17 16:00-17:00 南楼902教室
Abstract:

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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