Associated Laguerre Wavelets: Efficient Method to Solve Linear and Nonlinear Singular Initial and Boundary Value Problems

Wavelets have emerged as indispensable tools across various disciplines, renowned for their adaptability and effectiveness, particularly in signal processing and numerical analysis. Their application in approximating solutions for initial and boundary value problems has gained significant traction in recent years due to their precision in function approximation. This study introduces an innovative wavelet collocation approach tailored to address nonlinear singular initial value problems by leveraging associated Laguerre wavelets. These wavelets build upon the classical Laguerre wavelets, establishing the foundation for a novel collocation methodology. The proposed technique is applied to both linear and nonlinear singular boundary value problems, demonstrating its efficacy through extensive numerical experiments. The findings, presented through detailed graphs and tables, highlight the method's computational efficiency and accuracy. A comparative evaluation against established methods in the literature further validates the superior precision and robustness of the associated Laguerre wavelet collocation technique.