Lecture: Symplectic Schemes for Schrödinger and Klein-Gordon-Schrödinger Equations with Fractional Laplacian by Dr. Xiao Aiguo
Symplectic Schemes for Schrödinger and Klein-Gordon-Schrödinger Equations with Fractional Laplacian
Speaker: Xiao Aiguo
9:00-10:00 Oct 18, 2021
7215 No.7 Teaching Building
In this talk, we mainly introduce the symplectic scheme for the 1D space fractional Schrödinger 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-Schrödinger equations.
Brief Introduction of the Speaker:
Xiao Aiguo, professor, Doctoral Supervisor, Doctor of Science, Associated Dean of School of Mathematics and Computation Science, Xiangtan University, Deputy Director of Hunan Key Laboratory of Computational and Numerical Simulation of Science Engineering, Member of Academic Committee.
He presided National High Technology 836 project and was awarded second prize of Natural Science and First and Second prizes for outstanding teaching achievements in Hunan Province.
He has published more than 80 papers in famous academic journals, such as J. Comput. Phys., J. Sci. Comput., including more than 60 papers in SCI and EI.