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2022, Volume 30, Issue 10: 3825-3854. doi: 10.3934/era.2022195
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A high-order numerical scheme for right Caputo fractional differential equations with uniform accuracy

  • School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

  • Academic Editor: Xian-Ming Gu
  • Received: 18 June 2022 Revised: 17 August 2022 Accepted: 18 August 2022 Published: 24 August 2022

  • In this paper, we mainly study the high-order numerical scheme of right Caputo time fractional differential equations with uniform accuracy. Firstly, we construct the high-order finite difference method for the right Caputo fractional ordinary differential equations (FODEs) based on piecewise quadratic interpolation. The local truncation error of right Caputo FODEs is given, and the stability analysis of the right Caputo FODEs is proved in detail. Secondly, the time fractional partial differential equations (FPDEs) with right Caputo fractional derivative is studied by coupling the time-dependent high-order finite difference method and the spatial central second-order difference scheme. Finally, three numerical examples are used to verify that the convergence order of high-order numerical scheme is $ 3-\lambda $ in time with uniform accuracy.

    Citation: Li Tian, Ziqiang Wang, Junying Cao. A high-order numerical scheme for right Caputo fractional differential equations with uniform accuracy[J]. Electronic Research Archive, 2022, 30(10): 3825-3854. doi: 10.3934/era.2022195

    Related Papers:

  • In this paper, we mainly study the high-order numerical scheme of right Caputo time fractional differential equations with uniform accuracy. Firstly, we construct the high-order finite difference method for the right Caputo fractional ordinary differential equations (FODEs) based on piecewise quadratic interpolation. The local truncation error of right Caputo FODEs is given, and the stability analysis of the right Caputo FODEs is proved in detail. Secondly, the time fractional partial differential equations (FPDEs) with right Caputo fractional derivative is studied by coupling the time-dependent high-order finite difference method and the spatial central second-order difference scheme. Finally, three numerical examples are used to verify that the convergence order of high-order numerical scheme is $ 3-\lambda $ in time with uniform accuracy.


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