@article{Alqarni2026, 
author = {Mohammed Z. Alqarni and Mohamed A. Ramadan and Naglaa M. El-Shazly},
title = {A novel generalization of Chebyshev wavelet bases and its application to Bratu's boundary value problem},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {11634-11658},
keywords = {generalized Chebyshev wavelets, Bratu equation, computational flexibility, numerical collocation, accuracy},
url = {https://www.sciopen.com/article/10.3934/math.2026480},
doi = {10.3934/math.2026480},
abstract = {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    η-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.}
}