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Multiple Novels and Accurate Traveling Wave and Numerical Solutions of the (2+1) Dimensional Fisher-Kolmogorov- Petrovskii-Piskunov Equation

Author

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  • Mostafa M. A. Khater

    (Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
    Department of Mathematics, Obour High Institute for Engineering and Technology, Cairo 11828, Egypt
    These authors did all this work equally.)

  • Aliaa Mahfooz Alabdali

    (Faculty of Computing and information Technology Rabigh, King Abdulaziz University, Rabigh, Makkah 21911, Saudi Arabia
    These authors did all this work equally.)

Abstract

The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.), and trigonometric-quantic B-spline (TQBS) schemes. This model, which arises in population genetics and nematic liquid crystals, describes the reaction–diffusion system by traveling waves in population genetics and the propagation of domain walls, pattern formation in bi-stable systems, and nematic liquid crystals. Many novel analytical solutions are constructed. These solutions are used to evaluate the requested numerical technique’s conditions. The numerical solutions of the considered model are studied, and the absolute value of error between analytical and numerical is calculated to demonstrate the matching between both solutions. Some figures are represented to explain the obtained analytical solutions and the match between analytical and numerical results. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations.

Suggested Citation

  • Mostafa M. A. Khater & Aliaa Mahfooz Alabdali, 2021. "Multiple Novels and Accurate Traveling Wave and Numerical Solutions of the (2+1) Dimensional Fisher-Kolmogorov- Petrovskii-Piskunov Equation," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1440-:d:578597
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    References listed on IDEAS

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    1. Haiyong Qin & Mostafa M. A. Khater & Raghda A. M. Attia, 2020. "Copious Closed Forms of Solutions for the Fractional Nonlinear Longitudinal Strain Wave Equation in Microstructured Solids," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, April.
    2. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Abdel-Aty, Abdel-Haleem & Khater, Mostafa M.A. & Dutta, Hemen & Bouslimi, Jamel & Omri, M., 2020. "Computational solutions of the HIV-1 infection of CD4+T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
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    Cited by:

    1. Khater, Mostafa M.A., 2022. "Nonparaxial pulse propagation in a planar waveguide with Kerr–like and quintic nonlinearities; computational simulations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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