An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional Sine–Gordon equations

Zhiyong Xing, Liping Wen and Wansheng Wang

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 181, issue C, 624-641

Abstract: In this paper, we study the numerical solution of the Riesz space fractional Sine–Gordon equations. We develop an explicit fourth-order energy-preserving difference scheme for the two-dimensional space fractional Sine–Gordon equation (SGE). The conservation, convergence and boundedness properties of the numerical scheme are rigorously proved. Subsequently, the proposed numerical method is applied to approximate the one-dimensional space fractional SGE. Several numerical experiments are provided to verify the theoretical results.

Keywords: Sine–Gordon equation; Riesz fractional derivative; Explicit conservative numerical scheme; Fourth-order difference scheme; Convergence and stability (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:181:y:2021:i:c:p:624-641

DOI: 10.1016/j.matcom.2020.10.008

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