A numerical solution of the mathematical models for water pollution by shifted Jacobi polynomials

Abstract

Water pollution is one of the most significant environmental issues in developing countries, particularly in relation to drinking water quality. Therefore, monitoring and modeling the quality of water resources is very important in managing the exploitation and protection of water resources. This study presents a numerical approach for solving a mathematical model of soluble and insoluble water pollutants by utilizing shifted Jacobi polynomials (SJP). The transmissibility of water pollution was investigated using a system of ordinary differential equations. In this essay, a nonlinear system of ordinary differential equations is turned into an algebraic system by utilizing the collocation approach based on SJP. Finally, the Newton’s method is used to obtain numerical experiments. We also compared present method results by Runge-Kutta (RK) method to demonstrate the efficiency of the propounded method, which shows the results obtained are acceptable and in good agreement with the RK method.