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

Abstract

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.

Keywords:

• fractional Schrödinger equation
• shifted Grünwald–Letnikov formula
• weightedshifted Grünwald–Letnikov formulas
• fractional central difference
• energyconservation

2010 AMS Subject Classifications:

• 15A24
• 15A48
• 65H05
• 65F10
• 65F05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is financially supported by the Zhejiang Natural Science Foundation [grant number LQ12A01010].