A class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations.

In this work, we propose a class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations. We prove the energy conservation, stability, and convergence of our schemes. In the proposed schemes, we only need to solve linear algebraic systems to obtain the numerical solutions. Numerical examples are presented to verify the accuracy, energy conservation, and stability of these schemes. [ABSTRACT FROM PUBLISHER]