A Laguerre Wavelet‐Based Numerical Framework for Modeling and Analysis of Water Scarcity Dynamics With Real‐World Validation

ABSTRACT Water scarcity is a critical global issue with profound social, economic, and environmental consequences. Accurate modeling and efficient numerical techniques are important for predicting the dynamics of water scarcity over time. This study proposes a mathematical model for water scarcity and investigates its behavior using a numerical approach based on Laguerre wavelets (LW). The Laguerre wavelet method (LWM) is employed to approximate the solutions of the system, and its performance is compared with the well‐established Adams–Bashforth–Moulton (ABM) method and the classical fourth‐order Runge–Kutta (RK‐4) method. In addition, the model results for water resources are validated by comparison with real data from Chennai water resources. Error analysis reveals that the Laguerre wavelet method yields a smaller error when compared with the RK‐4 method than the ABM method does, demonstrating the superior accuracy and efficiency of the proposed approach. Furthermore, theoretical analyses concerning the convergence, existence, and boundedness of the solution are provided to ensure the reliability of the model. Numerical simulations, including both two‐dimensional and three‐dimensional graphical representations, further validate the accuracy of the technique. The results underscore the potential of Laguerre wavelets as an effective tool for solving complex real‐world problems such as water scarcity.