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Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model

Author

Listed:
  • Mohammed M. Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21577, Saudi Arabia)

  • Mohamed A. Abdelkawy

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi Arabia
    Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 2722165, Egypt)

  • António M. Lopes

    (Associated Laboratory for Energy, Transport and Aeronautics/Institute of Science and Innovation in Mechanical Engineering and Industrial Engineering (LAETA/INEGI), Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal)

Abstract

Applications of non-Newtonian fluids have been widespread across industries, accompanied by theoretical developments in engineering and mathematics. This paper studies a two-dimensional multi-term time fractional viscoelastic non-Newtonian fluid model by using two autonomous consecutive spectral collocation strategies. A modification of the spectral approach is implemented, leading to an algebraic system of equations able to obtain an approximate symmetric solution for the model. Numerical examples illustrate the effectiveness of the technique in terms of accuracy and convergence.

Suggested Citation

  • Mohammed M. Al-Shomrani & Mohamed A. Abdelkawy & António M. Lopes, 2023. "Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2078-:d:1134831
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    References listed on IDEAS

    as
    1. M. A. Abdelkawy & Mohammed M. Babatin & Abeer S. Alnahdi & T. M. Taha, 2022. "Legendre spectral collocation technique for fractional inverse heat conduction problem," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-15, May.
    2. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    3. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. M. A. Abdelkawy, 2021. "Numerical solutions for fractional initial value problems of distributed-order," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(07), pages 1-13, July.
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