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

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  • 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
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    References listed on IDEAS

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    4. 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.
    5. 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.
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