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2022, Volume 30, Issue 4: 1263-1281. doi: 10.3934/era.2022066
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Numerical analysis of variable-order fractional KdV-Burgers-Kuramoto equation

  • 1.
    College of Science, Henan University of Technology, Zhengzhou 450001, China
  • 2.
    School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 3.
    School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441000, China

  • Academic Editor: Xian-Ming Gu
  • Received: 25 December 2021 Revised: 19 February 2022 Accepted: 09 March 2022 Published: 16 March 2022

  • In this paper, a fully discrete local discontinuous Galerkin finite element method is proposed to solve the KdV-Burgers-Kuramoto equation with variable-order Riemann-Liouville time fractional derivative. The method proposed in this paper is based on the finite difference method in time and local discontinuous Galerkin method in space. For all $ \epsilon(t)\in (0, 1) $ with variable order, we prove the scheme is unconditional stable and convergent. Finally, numerical examples are provided to verify the theoretical analysis and the order of convergence for the proposed method.

    Citation: Leilei Wei, Xiaojing Wei, Bo Tang. Numerical analysis of variable-order fractional KdV-Burgers-Kuramoto equation[J]. Electronic Research Archive, 2022, 30(4): 1263-1281. doi: 10.3934/era.2022066

    Related Papers:

  • In this paper, a fully discrete local discontinuous Galerkin finite element method is proposed to solve the KdV-Burgers-Kuramoto equation with variable-order Riemann-Liouville time fractional derivative. The method proposed in this paper is based on the finite difference method in time and local discontinuous Galerkin method in space. For all $ \epsilon(t)\in (0, 1) $ with variable order, we prove the scheme is unconditional stable and convergent. Finally, numerical examples are provided to verify the theoretical analysis and the order of convergence for the proposed method.


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