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

Min Li; Ju Ming; Tingting Qin; Boya Zhou; Min Li; Ju Ming; Tingting Qin; Boya Zhou

doi:10.3934/nhm.2023042

Networks and Heterogeneous Media

2023, Volume 18, Issue 3: 957-981. doi: 10.3934/nhm.2023042

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

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
2.
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
3.
School of Mathematics and Big Data, Foshan University, Guangdong, 52800, China

Received: 28 December 2022 Revised: 25 February 2023 Accepted: 05 March 2023 Published: 21 March 2023

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.
Citation: Min Li, Ju Ming, Tingting Qin, Boya Zhou. Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations[J]. Networks and Heterogeneous Media, 2023, 18(3): 957-981. doi: 10.3934/nhm.2023042

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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.

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