A wavelet-based collocation approach for solving chlorine transport model

This study provides a unified framework for analyzing the two-dimensional chlorine transport model in pipes, governed by a second-order partial differential equation with complex boundary conditions. Previous analytical solutions have used the Laplace transform in conjunction with the residue method to obtain results in the form of Bessel or Mittag-Leffler functions for integer- and fractional-order models, respectively. In this paper, the Haar wavelet collocation method is applied to solve the governing equation of the chlorine transport model. The obtained numerical results are then compared with the corresponding exact solution to assess the accuracy, reliability, and computational efficiency of the method. This method provides a simple and versatile tool for simulating chlorine transport in water distribution systems under various boundary conditions. The behavior of $\psi (\lambda )$ is examined using Haar collocation points, and the resulting eigenvalue distributions are presented through graphical and numerical comparisons. Additionally, a parametric study is conducted to analyze chlorine decay, revealing the influence of governing parameters on concentration attenuation. This assertion combines analytical insights from both integer and fractional-order models, establishing the Haar wavelet collocation method as a strong, practical alternative for tackling such transport problems.