Numerical solution of some class of differential equations by Galerkin method utilizing Boubaker wavelets

This paper proposes a Galerkin method based on Boubaker wavelets (BWGM) for the numerical solution of a class of differential equations. The method employs Boubaker wavelets as both weight functions and basis elements to construct approximate solutions. The accuracy of the proposed method is evaluated by comparing numerical results with exact solutions and with existing schemes such as the Galerkin method using Fibonacci and Gegenbauer wavelets. Several examples are provided to demonstrate the validity and applicability of the method. The results indicate that BWGM yields high accuracy with minimal absolute error, making it an efficient tool for solving linear, singular, and nonlinear boundary value problems.