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Research Article | Open Access

Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations

Min Li1, Ju Ming2, Tingting Qin2, Boya Zhou3( )
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
School of Mathematics and Big Data, Foshan University, Guangdong, 52800, China
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Abstract

An energy-preserving finite difference method is first presented for solving the nonlinear coupled space-fractional Klein-Gordon (KG) equations. The discrete conservation law, boundedness of the numerical solutions and convergence of the numerical schemes are obtained. These results are proved by the recent developed fractional Sobolev inequalities, the matrix analytical methods and so on. Numerical experiments are carried out to confirm the theoretical findings.

Keywords

nonlinear coupled space-fractional KG equationsenergy-preserving finite difference methodGlobal consistency analysisthe discrete conservation law

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Networks and Heterogeneous Media
Volume 18 Issue 3,
September 2023
Pages 957-981
DOI: 10.3934/nhm.2023042

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Cite this article:
Li M, Ming J, Qin T, et al. Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations. Networks and Heterogeneous Media, 2023, 18(3): 957-981. https://doi.org/10.3934/nhm.2023042

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Received: 28 December 2022
Revised: 25 February 2023
Accepted: 05 March 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)