Structure-preserving scheme for one dimension and two dimension fractional KGS equations
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Published:2023
Issue:1
Volume:18
Page:463-493
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ISSN:1556-1801
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Container-title:Networks and Heterogeneous Media
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language:
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Short-container-title:NHM
Author:
Wang Junjie1, Zhang Yaping2, Zhai Liangliang3
Affiliation:
1. School of Mathematics and Statistical, Pu'er University, Yunnan, 665000, China 2. School of Science, Shaoyang University, Hunan, 422000, China 3. School of Science, Xi'an Shiyou University, Shaanxi, 710065, China
Abstract
<abstract><p>In the paper, we study structure-preserving scheme to solve general fractional Klein-Gordon-Schrödinger equations, including one dimension case and two dimension case. First, the high central difference scheme and Crank-Nicolson scheme are used to one dimension fractional Klein-Gordon-Schrödinger equations. We show that the arising scheme is uniquely solvable, and approximate solutions converge to the exact solution at the rate $ O(\tau^2+h^4) $. Moreover, we prove that the resulting scheme can preserve the mass and energy conservation laws. Second, we show Crank-Nicolson scheme for two dimension fractional Klein-Gordon-Schrödinger equations, and the proposed scheme preserves the mass and energy conservation laws in discrete formulations. However, the obtained discrete system is nonlinear system. Then, we show a equivalent form of fractional Klein-Gordon-Schrödinger equations by introducing some new auxiliary variables. The new system is discretized by the high central difference scheme and scalar auxiliary variable scheme, and a linear discrete system is obtained, which can preserve the energy conservation law. Finally, the numerical experiments including one dimension and two dimension fractional Klein-Gordon-Schrödinger systems are given to verify the correctness of theoretical results.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability
Reference27 articles.
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