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A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation

Author

Listed:
  • Yuejie Li

    (Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China
    School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China)

  • Zhendong Luo

    (School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
    School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

Abstract

We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method.

Suggested Citation

  • Yuejie Li & Zhendong Luo, 2023. "A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4699-:d:1283686
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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. Baseri, A. & Abbasbandy, S. & Babolian, E., 2018. "A collocation method for fractional diffusion equation in a long time with Chebyshev functions," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 55-65.
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