A Conservative Crank-Nicolson Fourier Spectral Method for the Space Fractional Schrödinger Equation with Wave Operators. (9th June 2021)

• Record Type: Journal Article
• Authors: Zhang, Lei; Yang, Rui; Zhang, Li; Wang, Lisha
• Other Names: Zhang Xinguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-06-09
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/5137845
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, the Crank-Nicolson Fourier spectral method is proposed for solving the space fractional Schrödinger equation with wave operators. The equation is treated with the conserved Crank-Nicolson Fourier Galerkin method and the conserved Crank-Nicolson Fourier collocation method, respectively. In addition, the ability of the constructed numerical method to maintain the conservation of mass and energy is studied in detail. Meanwhile, the convergence with spectral accuracy in space and second-order accuracy in time is verified for both Galerkin and collocation approximations. Finally, the numerical experiments verify the properties of the conservative difference scheme and demonstrate the correctness of theoretical results.