A conservative spectral Galerkin method for the coupled nonlinear space-fractional Schrödinger equations. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Wang, Ying; Mei, Liquan
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 12(2019)
• Page Start: 2387
• Page End: 2410
• Publication Date: 2019-12-02
• Subjects: Coupled nonlinear space-fractional Schrödinger equations -- Crank-Nicolson method -- Legendre spectral Galerkin method -- mass and energy conservation laws -- spectral accuracy; 65M06 -- 65M12 -- 65M15 -- 65M70; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1563687
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, a conservative spectral Galerkin method, which is based on the Crank-Nicolson method for the temporal discretization and Legendre spectral Galerkin method for the spatial discretization, is proposed to solve the coupled nonlinear space-fractional Schrödinger equations. We proved that the proposed method satisfies the mass and energy conservation laws in the discrete sense. Moreover, a rigorous analysis of the unique solvability and optimal error estimate in the L 2 -norm of the Crank-Nicolson spectral Galerkin method are derived. In order to compute the nonlinear system efficiently, we introduce a linear iterative algorithm in implementation. A series of numerical experiments are carried out to illustrate the efficiency of the method.