Affiliation of Author(s):数学学院

Journal:Zeitschrift für Angewandte Mathematik und Mechanik

Key Words:convergence analysis; fast Fourier transform; Fourier spectral method; mass and energy conservation laws; nonlinear coupled space fractional Klein-Gordon-Schrodinger equations

Abstract:In this paper, we give an efficient numerical method for the nonlinear coupled space fractional Klein-Gordon-Schrodinger (NCSFKGS) equations, based on the Crank-Nicolson method, the central difference method and the Fourier spectral method. As far as we know, no one has studied the Equations (5)-(6) in our paper, these equations are different from those in [39] which only considers space fractional Schrodinger equation while the Klein-Gordon equation is classical, here, we consider the two equations which are both space fractional. In this paper, the Crank-Nicolson method and the central difference method are used to discretize the space fractional Schrodinger equation and the space fractional Klein-Gordon equation in time direction, respectively. The Fourier spectral method is used to discretize the NCSFKGS equations in space direction. This numerical method conserves the mass and energy in the discrete level. The convergence of the numerical method is of second order accuracy in time and spectral accuracy in space. Rigorous proofs are developed here for the conservation laws and the convergence of the numerical method. Numerical experiments are presented to confirm the theoretical results and they proved that our numerical method is very efficient (it only takes a few seconds to get the numerical solutions).

All the Authors:杨秀,张慧

First Author:贾俊青

Indexed by:Unit Twenty Basic Research

Correspondence Author:蒋晓芸

Discipline:Natural Science

First-Level Discipline:Mathematics

Volume:100

Issue:2

Page Number:e201800314

Translation or Not:no

Date of Publication:2019-12-01

Included Journals:SCI