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

作者：Hongling Hu, Xianlin Jin, Dongdong He, Kejia Pan, Qifeng Zhang · 发表于：Numerical Methods for Partial Differential Equations · 年份：2021 · DOI：10.1002/num.22788 · 被引用次数：6 · 研究领域：Fractional Differential Equations Solutions、Numerical methods for differential equations、Differential Equations and Numerical Methods

Abstract In this paper, a linearized semi‐implicit finite difference scheme is proposed for solving the two‐dimensional (2D) space fractional nonlinear Schrödinger 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.