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

Sıla Övgü Korkut

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 209, issue C, 324-341

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.

Keywords: Taylor wavelets; Burgers–Huxley equation; Convergence analysis; Non-linear partial differential equations (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:209:y:2023:i:c:p:324-341

DOI: 10.1016/j.matcom.2023.02.019

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