A high-accuracy compact finite difference scheme for time-fractional diffusion equations

• Xindong Zhang ^[1] ; Hanxiao Wang ^[2] ; Ziyang Luo ^[4] ; Leilei Wei ^[3]
  1. [1] Guizhou University of Finance and Economics

     Guizhou University of Finance and Economics

     China

     
  2. [2] Xinjiang Normal University

     Xinjiang Normal University

     China

     
  3. [3] Henan University of Technology

     Henan University of Technology

     China

     
  4. [4] School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, 830023, People’s Republic of China

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 2, 2025, págs. 589-609
• Idioma: inglés
• DOI: 10.33044/revuma.4665
• Enlaces
  • Texto completo
• Resumen

  • We propose a compact finite difference (CFD) scheme for the solution of time-fractional diffusion equations (TFDE) with the Caputo–Fabrizio derivative. The Caputo–Fabrizio derivative is discussed in the time direction and is discretized by a special discrete scheme. The compact difference operator is introduced in the space direction. We prove the unconditional stability and convergence of the proposed scheme. We show that the convergence order is O(τ3 + h4), where τ and h are the temporal stepsize and spatial stepsize, respectively. Our main purpose is to show that the Caputo–Fabrizio derivative without singular term can improve the accuracy of the discrete scheme.

    Numerical examples demonstrate the efficiency of the proposed method, and the numerical results agree well with the theoretical predictions.

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