Year: 2021
Author: Longbin Wu, Qiang Ma, Xiaohua Ding
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 560–579
Abstract
This paper deals with the Crank-Nicolson Fourier collocation method for the nonlinear fractional Schrödinger equation containing a fractional derivative. We prove that at each discrete time the method preserves the discrete mass and energy conservation laws. The existence, uniqueness and convergence of the numerical solution are also investigated. In particular, we show that the method has the second-order accuracy in time and the spectral accuracy in space. Since the proposed schemes are implicit, they are solved by an iteration algorithm with FFT. Two examples illustrate the efficiency and accuracy of the numerical schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.110920.060121
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 3 : pp. 560–579
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Crank-Nicolson Fourier collocation method nonlinear fractional Schrödinger equation conservation laws existence and uniqueness convergence.