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

2019/10/18 by Hongling Hu, Xianlin Jin, Hu, Hongling +7
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1910.08311

openalex publication_date 2019/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 on 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 and proved 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.

Citations

• Some solutions to the space fractional Schrödinger equation using momentum representation method

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