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Exponentially fitted methods for solving time fractional nonlinear reaction–diffusion equation

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  • Zahra, W.K.
  • Nasr, M.A.
  • Van Daele, M.

Abstract

In this article, we will develop a new numerical scheme with the second order in time and a class of fourth order or sixth order in space based on the exponential fitting techniques to approximate the nonlinear time fractional reaction–diffusion equation with fixed order and distributed order derivatives. These techniques depend on a parameter, which will be used to annihilate the error and increase the order of accuracy. The proposed methods are proved to be unconditionally stable and convergent by Fourier analysis. Also, the theoretical results and the effectiveness of the numerical scheme are confirmed by numerical test problems and a comparison with other methods is presented.

Suggested Citation

  • Zahra, W.K. & Nasr, M.A. & Van Daele, M., 2019. "Exponentially fitted methods for solving time fractional nonlinear reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 468-490.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:468-490
    DOI: 10.1016/j.amc.2019.04.019
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
    2. Owolabi, Kolade M., 2016. "Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 89-98.
    3. Fenghui Huang, 2012. "A Time-Space Collocation Spectral Approximation for a Class of Time Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-19, September.
    4. Zahra, W.K. & Van Daele, M., 2017. "Discrete spline methods for solving two point fractional Bagley–Torvik equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 42-56.
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    Cited by:

    1. Saffarian, Marziyeh & Mohebbi, Akbar, 2021. "Numerical solution of two and three dimensional time fractional damped nonlinear Klein–Gordon equation using ADI spectral element method," Applied Mathematics and Computation, Elsevier, vol. 405(C).

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