High-order conservative scheme for the coupled space fractional nonlinear Schrödinger equations

Abstract

In this paper, an efficient finite difference scheme is proposed for one dimension and two dimension coupled space fractional nonlinear Schrödinger equations. First, the high-order difference scheme and Crank–Nicolson scheme are used to one dimension coupled space fractional nonlinear Schrödinger equations. second, we show that the high-order conservative difference scheme satisfies the mass and energy conservation laws respectively, and convergence and unconditional stability of the scheme are also proved. Next, we give the high-order conservative scheme for two dimension coupled space fractional nonlinear Schrödinger equations. Finally, some numerical results are reported to verify our theoretical analysis.

Keywords:

• Fractional nonlinear Schrödinger equations
• conservation law
• Crank–Nicolson scheme
• convergence

2010 Mathematics Subject Classification:

• 65N06

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by National Natural Science Foundation of China (Grant No. 11801441) and Natural Science Foundation of Shaanxi Province No. 2020JM-425.