A collocation approach to solving the model of pollution for a system of lakes

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. In this paper, the pollution problem of three lakes with interconnecting channels has been studied. A collocation method is presented to solve modeling the pollution of a system of lakes by a system of differential equations. By using Bessel polynomials and collocation points, this method transforms modeling the pollution of a system of lakes into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. A numerical example is included to demonstrate the validity and applicability of the technique. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB.