Abstract: This paper investigates a pollution model for a closed system consisting of three physically interconnected lakes. The pollutant source enters the first lake, while the exchange of contaminants among the lakes is described by a coupled system of first-order differential equations. To obtain accurate numerical solutions, the Smooth Composite Shifted Legendre Pseudospectral Method is applied. The contamination levels in each lake are examined under three pollutant loading scenarios: impulsive, exponentially decaying, and periodic inputs. The convergence and error of the method are analyzed. Numerical results and residual errors are compared with those obtained from established methods in the literature to assess the accuracy and stability of the scheme. The results demonstrate that the proposed approach yields reliable and efficient approximations, indicating that it can serve as a practical numerical tool for modeling pollutant transport in interconnected lake systems and supporting water quality assessment studies.

Keywords: Water Pollution Management, Lake Contamination, Shifted Legendre Spectral Method, Numerical Simulation, Error Estimation, Residual Analysis

Pages: 476-483