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AIMS Mathematics

2026, Volume 11, Issue 4: 11634-11658. doi: 10.3934/math.2026480
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Research article

A novel generalization of Chebyshev wavelet bases and its application to Bratu's boundary value problem

  • 1.
    Department of Mathematics, King Khalid University, Abha, Saudi Arabia
  • 2.
    Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebien El-Koom, Menoufia, Egypt
  • Published: 27 April 2026

  • MSC : 42C40, 65L10, 65T60

  • This paper aims to examine a newly proposed, more flexible, and thorough definition of a novel generalization of Chebyshev wavelet basis functions, possessing more computational flexibility and resolution by analyzing its properties. A proficient collocation technique is developed to examine the nonlinear Bratu boundary-value problem, which has recently emerged in combustion and chemical reaction theory. The differential equation is transformed into a system of nonlinear algebraic equations, after which the efficacy of the method is evaluated using the $ \eta $-base wavelet in comparison to other numerical instances, exact solutions, and other analytical techniques. According to the results, this method offers a reliable and flexible tool for handling challenging boundary-value issues in scientific computing.

    Citation: Mohammed Z. Alqarni, Mohamed A. Ramadan, Naglaa M. El-Shazly. A novel generalization of Chebyshev wavelet bases and its application to Bratu's boundary value problem[J]. AIMS Mathematics, 2026, 11(4): 11634-11658. doi: 10.3934/math.2026480

    Related Papers:

  • This paper aims to examine a newly proposed, more flexible, and thorough definition of a novel generalization of Chebyshev wavelet basis functions, possessing more computational flexibility and resolution by analyzing its properties. A proficient collocation technique is developed to examine the nonlinear Bratu boundary-value problem, which has recently emerged in combustion and chemical reaction theory. The differential equation is transformed into a system of nonlinear algebraic equations, after which the efficacy of the method is evaluated using the $ \eta $-base wavelet in comparison to other numerical instances, exact solutions, and other analytical techniques. According to the results, this method offers a reliable and flexible tool for handling challenging boundary-value issues in scientific computing.



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  • © 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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