A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrodinger equations

In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schrodinger equation (SFNSE). The scheme has the property of mass and energy conservation at the discrete level, with an unconditional stability and a second-order accuracy for both time and spatial variables. The main contribution of this paper is an optimal pointwise error estimate for the 2D SFNSE, which is rigorously established for the first time. Moreover, a novel technique is proposed for dealing with the nonlinear term in the equation, which plays an essential role in the error estimation. Finally, the numerical results confirm well with the theoretical findings.

Automated summary

This paper introduces a linearized semi-implicit finite difference scheme for solving the two-dimensional space fractional nonlinear Schrodinger equation, which is characterized by mass and energy conservation, stability, and high accuracy. The optimal pointwise error estimate for the equation is rigorously established for the first time, along with a novel technique for handling the nonlinear term. The numerical results validate the theoretical findings.