IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v209y2023icp324-341.html
   My bibliography  Save this article

An accurate and efficient numerical solution for the generalized Burgers–Huxley equation via Taylor wavelets method: Qualitative analyses and Applications

Author

Listed:
  • Korkut, Sıla Övgü

Abstract

This paper aims to propose a highly accurate and simple algorithm based on the Taylor wavelet methods for obtaining the approximate solution of the generalized Burgers–Huxley equation. Additionally, various qualitative analyses including positivity-preservation, monotonicity-preservation, boundedness of the obtained solutions as well as convergence analysis of the proposed method have been provided. Furthermore, the applicability and validity of the proposed method are demonstrated on a benchmark equation. By comparing the approximate solutions with the exact solution, it is observed that the proposed method has recorded better results than the other methods in the literature. Although the generalized Burgers–Huxley equation has been studied throughout the study, it is worth emphasizing that the proposed method is a good solver for such nonlinear equations.

Suggested Citation

  • Korkut, Sıla Övgü, 2023. "An accurate and efficient numerical solution for the generalized Burgers–Huxley equation via Taylor wavelets method: Qualitative analyses and Applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 324-341.
    • Handle: RePEc:eee:matcom:v:209:y:2023:i:c:p:324-341
    DOI: 10.1016/j.matcom.2023.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423000927
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.02.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. Nawaz & H. Ullah & S. Islam & M. Idrees, 2013. "Application of Optimal Homotopy Asymptotic Method to Burger Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, July.
    2. Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
    3. Shiralashetti, S.C. & Kumbinarasaiah, S., 2017. "Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 591-602.
    4. Murat Sari & Gürhan Gürarslan, 2009. "Numerical Solutions of the Generalized Burgers-Huxley Equation by a Differential Quadrature Method," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-11, April.
    5. Batiha, B. & Noorani, M.S.M. & Hashim, I., 2008. "Application of variational iteration method to the generalized Burgers–Huxley equation," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 660-663.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    2. Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
    3. Jaiswal, Shubham & Chopra, Manish & Das, S., 2019. "Numerical solution of non-linear partial differential equation for porous media using operational matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 138-154.
    4. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    5. Fesanghary, M. & Pirbodaghi, T. & Asghari, M. & Sojoudi, H., 2009. "A new analytical approximation to the Duffing-harmonic oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 571-576.
    6. Yadav, Swati & Pandey, Rajesh K., 2020. "Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Duan, Yali & Kong, Linghua & Zhang, Rui, 2012. "A lattice Boltzmann model for the generalized Burgers–Huxley equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 625-632.
    8. Izadi, Mohammad, 2021. "A discontinuous finite element approximation to singular Lane-Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    9. Hassan, M.M. & Abdel-Razek, M.A. & Shoreh, A.A.-H., 2015. "Explicit exact solutions of some nonlinear evolution equations with their geometric interpretations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 243-252.
    10. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    11. S., Kumbinarasaiah & G., Manohara & G., Hariharan, 2023. "Bernoulli wavelets functional matrix technique for a system of nonlinear singular Lane Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 133-165.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:209:y:2023:i:c:p:324-341. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.