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A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques

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  • Agarwal, P.
  • Deni̇z, S.
  • Jain, S.
  • Alderremy, A.A.
  • Aly, Shaban

Abstract

In this work, we propose a new optimal perturbation iteration method for solving the generalized Fitzhugh–Nagumo equation with time-dependent coefficients. This research reveals that the new proposed technique, with the aid of symbolic computations, provides a straightforward and impressive mathematical tool for solving nonlinear partial differential equations. Implementing this method to Fitzhugh–Nagumo equation illustrates its potency. Convergence analysis also shows that OPIM, unlike many other methods in literature, converges fast to exact analytical solutions of the nonlinear problems at lower order of approximations.

Suggested Citation

  • Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119315730
    DOI: 10.1016/j.physa.2019.122769
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    References listed on IDEAS

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    1. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    2. Arqub, Omar Abu & Maayah, Banan, 2018. "Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 117-124.
    3. Abdon Atangana & Aydin Secer, 2013. "The Time-Fractional Coupled-Korteweg-de-Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
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    Cited by:

    1. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Izadi, Mohammad & Roul, Pradip, 2022. "Spectral semi-discretization algorithm for a class of nonlinear parabolic PDEs with applications," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    3. Mondal, Argha & Mistri, Kshitish Ch. & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar, 2021. "An analytical scheme on complete integrability of 2D biophysical excitable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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