An energy conservative difference scheme for the nonlinear fractional Schrodinger equations

作者：Wang, Pengde; Huang, Chengming^*

来源：Journal of Computational Physics, 2015, 293: 238-251.

DOI：10.1016/j.jcp.2014.03.037

• Fractional Schrodinger equation
• Crank-Nicolson scheme
• Conservation
• Solvability
• Convergence

In this paper, an energy conservative Crank-Nicolson difference scheme for nonlinear Riesz space-fractional Schrodinger equations is studied. We give a rigorous analysis of the conservation properties, including mass conservation and energy conservation in the discrete sense. Based on Brouwer fixed point theorem, the existence of the difference solution is proved. By virtue of the energy method, the difference solution is shown to be unique and convergent at the order of 0 (tau(2) + h(2)) in the l(2)-norm with time step tau and mesh size h. Finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results.

• 单位
  华中科技大学