A class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations. Issue 3 (3rd March 2016)

• Record Type: Journal Article
• Authors: Yang, Zheng
• Is Part Of: International journal of computer mathematics. Volume 93:Issue 3(2016)
• Page Start: 609
• Page End: 626
• Publication Date: 2016-03-03
• Subjects: fractional Schrödinger equation -- shifted Grünwald–Letnikov formula -- weightedshifted Grünwald–Letnikov formulas -- fractional central difference -- energyconservation; 15A24 -- 15A48 -- 65H05 -- 65F10 -- 65F05; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1009904
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this work, we propose a class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations. We prove the energy conservation, stability, and convergence of our schemes. In the proposed schemes, we only need to solve linear algebraic systems to obtain the numerical solutions. Numerical examples are presented to verify the accuracy, energy conservation, and stability of these schemes.