Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations

Junjie Wang and Aiguo Xiao

Applied Mathematics and Computation, 2019, vol. 350, issue C, 348-365

Abstract: In this paper, we propose Fourier spectral method to solve space fractional Klein–Gordon–Schrödinger equations with periodic boundary condition. First, the semi-discrete scheme is given by using Fourier spectral method in spatial direction, and conservativeness and convergence of the semi-discrete scheme are discussed. Second, the fully discrete scheme is obtained based on Crank–Nicolson/leap-frog methods in time direction. It is shown that the scheme can be decoupled, and preserves mass and energy conservation laws. It is proven that the scheme is of the accuracy O(τ2+N−r). Last, based on the numerical experiments, the correctness of theoretical results is verified, and the effects of the fractional orders α, β on the solitary solution behaviors are investigated. In particular, some interesting phenomena including the quantum subdiffusion are observed, and complex dynamical behaviors are shown clearly by many intuitionistic images.

Keywords: Space fractional Klein–Gordon–Schrödinger equations; Fourier spectral method; Stability; Convergence; Conservativeness; Quantum subdiffusion (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031831107X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:348-365

DOI: 10.1016/j.amc.2018.12.046

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().