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

  • 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

    Related Papers:

  • 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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