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

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.