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Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method

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  • Dwivedi, Kushal Dhar
  • Singh, Jagdev

Abstract

A new finite difference collocation algorithm has been introduced with the help of Fibonacci polynomial and then applied to one super and two sub-diffusion problems having an exact solution. It has also been shown that numerical error obtained with the investigated method is more accurate than previously existing methods. Fractional order reaction advection sub-diffusion equation containing Caputo and Riemann–Liouville fractional derivatives has been solved and the effects due to change in various parameters presented in the considered model with the graphical representation have been discussed.

Suggested Citation

  • Dwivedi, Kushal Dhar & Singh, Jagdev, 2021. "Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 38-50.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:38-50
    DOI: 10.1016/j.matcom.2020.09.008
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    References listed on IDEAS

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    1. Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Hassani, Hossein & Avazzadeh, Zakieh, 2019. "Transcendental Bernstein series for solving nonlinear variable order fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Ayşe Betül Koç & Musa Çakmak & Aydın Kurnaz, 2014. "A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-5, August.
    4. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    5. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
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    1. H. Mesgarani & M. Bakhshandeh & Y. Esmaeelzade Aghdam & J. F. Gómez-Aguilar, 2023. "The Convergence Analysis of the Numerical Calculation to Price the Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1845-1856, December.

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