An efficient numerical approach to solve Schrödinger equations with space fractional derivative. (4th January 2019)

• Record Type: Journal Article
• Authors: Zhang, Jun; Lin, Shimin; Wang, JinRong
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 5(2019)
• Page Start: 1596
• Page End: 1608
• Publication Date: 2019-01-04
• Subjects: conservation -- error estimate -- Schrödinger equations -- space‐fractional order; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5459
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We design and analyze an efficient numerical approach to solve the coupled Schrödinger equations with space‐fractional derivative. The numerical scheme is based on leap‐frog in time direction and Fourier method in spatial direction. The advantage of the numerical scheme is that only a linear equation needs to be solved for each time step size, and we proved that the energy and mass of space‐fractional coupled Schrödinger equations (SFCSEs) are conserved in the case of full‐discrete scheme. Moreover, we also analyze the error estimate of the numerical scheme, and numerical solutions converge with the order O ( △ t 2 + N − s ) in L 2 norm. Numerical examples are illustrated to verify the theoretical results.