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Networks and Heterogeneous Media

2023, Volume 18, Issue 1: 291-309. doi: 10.3934/nhm.2023011
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Effective difference methods for solving the variable coefficient fourth-order fractional sub-diffusion equations

  • 1.
    School of Mathematical Sciences and V.C. and V.R. Key Lab, Sichuan Normal University, Chengdu 610068, China
  • 2.
    School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
  • 3.
    School of Mathematics, Aba Teachers University, Aba 623002, China
  • Received: 21 September 2022 Revised: 13 November 2022 Accepted: 05 December 2022 Published: 21 December 2022

  • This paper is concerned with the numerical approximations for the variable coefficient fourth-order fractional sub-diffusion equations subject to the second Dirichlet boundary conditions. We construct two effective difference schemes with second order accuracy in time by applying the second order approximation to the time Caputo derivative and the sum-of-exponentials approximation. By combining the discrete energy method and the mathematical induction method, the proposed methods proved to be unconditional stable and convergent. In order to overcome the possible singularity of the solution near the initial stage, a difference scheme based on non-uniform mesh is also given. Some numerical experiments are carried out to support our theoretical results. The results indicate that the our two main schemes has the almost same accuracy and the fast scheme can reduce the storage and computational cost significantly.

    Citation: Zhe Pu, Maohua Ran, Hong Luo. Effective difference methods for solving the variable coefficient fourth-order fractional sub-diffusion equations[J]. Networks and Heterogeneous Media, 2023, 18(1): 291-309. doi: 10.3934/nhm.2023011

    Related Papers:

  • This paper is concerned with the numerical approximations for the variable coefficient fourth-order fractional sub-diffusion equations subject to the second Dirichlet boundary conditions. We construct two effective difference schemes with second order accuracy in time by applying the second order approximation to the time Caputo derivative and the sum-of-exponentials approximation. By combining the discrete energy method and the mathematical induction method, the proposed methods proved to be unconditional stable and convergent. In order to overcome the possible singularity of the solution near the initial stage, a difference scheme based on non-uniform mesh is also given. Some numerical experiments are carried out to support our theoretical results. The results indicate that the our two main schemes has the almost same accuracy and the fast scheme can reduce the storage and computational cost significantly.


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