A conservative spectral Galerkin method for the coupled nonlinear space-fractional Schr?dinger equations

作者：Wang, Ying; Mei, Liquan^*

来源：International Journal of Computer Mathematics, 2019, 96(12): 2387-2410.

DOI：10.1080/00207160.2018.1563687

• Coupled nonlinear space-fractional Schr?dinger equations
• Crank-Nicolson method
• Legendre spectral Galerkin method
• mass and energy conservation laws
• spectral accuracy

In this paper, a conservative spectral Galerkin method, which is based on the Crank-Nicolson method for the temporal discretization and Legendre spectral Galerkin method for the spatial discretization, is proposed to solve the coupled nonlinear space-fractional Schr?dinger equations. We proved that the proposed method satisfies the mass and energy conservation laws in the discrete sense. Moreover, a rigorous analysis of the unique solvability and optimal error estimate in the -norm of the Crank-Nicolson spectral Galerkin method are derived. In order to compute the nonlinear system efficiently, we introduce a linear iterative algorithm in implementation. A series of numerical experiments are carried out to illustrate the efficiency of the method.

• 出版日期2019-12-2
• 单位西安交通大学