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An Unchanged Basis Function and Preserving Accuracy Crank–Nicolson Finite Element Reduced-Dimension Method for Symmetric Tempered Fractional Diffusion Equation

Author

Listed:
  • Xiaoyong Yang

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

  • Zhendong Luo

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

Abstract

We herein mainly employ a proper orthogonal decomposition (POD) to study the reduced dimension of unknown solution coefficient vectors in the Crank–Nicolson finite element (FE) (CNFE) method for the symmetric tempered fractional diffusion equation so that we can build the reduced-dimension recursive CNFE (RDRCNFE) method. In this case, the RDRCNFE method keeps the same basic functions and accuracy as the CNFE method. Especially, we adopt the matrix analysis to discuss the stability and convergence of RDRCNFE solutions, resulting in the very laconic theoretical analysis. We also use some numerical simulations to confirm the correctness of theoretical results.

Suggested Citation

  • Xiaoyong Yang & Zhendong Luo, 2022. "An Unchanged Basis Function and Preserving Accuracy Crank–Nicolson Finite Element Reduced-Dimension Method for Symmetric Tempered Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3630-:d:933447
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    References listed on IDEAS

    as
    1. Zhendong Luo, 2022. "The Dimensionality Reduction of Crank–Nicolson Mixed Finite Element Solution Coefficient Vectors for the Unsteady Stokes Equation," Mathematics, MDPI, vol. 10(13), pages 1-11, June.
    2. Zhendong Luo, 2022. "A Finite Element Reduced-Dimension Method for Viscoelastic Wave Equation," Mathematics, MDPI, vol. 10(17), pages 1-12, August.
    3. Zhendong Luo, 2020. "The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation," Mathematics, MDPI, vol. 8(8), pages 1-11, August.
    4. Xing, Zhiyong & Wen, Liping, 2019. "Numerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 155-166.
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