A Novel Scheme for the Solution of Differential Equations Through Müntz-Legendre Wavelets

This study aims to present a numerical wavelet-based approach for solving both lower-order and higher-order differential equations. This approach is characterized by the use of Miintz- Legendre wavelets (MLWs) for estimation. The MLW is considered by the Muntz-Legendre polynomials (MLPs), which has orthogonal properties. Firstly, MLW is introduced after which an integral operational matrix is derived. By utilizing this operational matrix, the original differential equation is reformulated into a system of algebraic equations with involved unknown coefficients associated with the Muntz-Legendre wavelets (MLWs), which are determined through further calculations to approximate the solution accurately. The effectiveness and accuracy of the proposed technique are validated using specific numerical examples.