Application of numerical integration in solving a reverse osmosis model

Abstract

Clean water is always needed for human living. Due to pollution, we often need to purify water. One way to do so is using the reverse osmosis system. A mathematical model for the reverse osmosis system has been obtained. In this paper, we show the importance of numerical methods in solving the reverse osmosis model. In particular, we focus on the application of numerical integration methods in the process of solving the model. We consider three types of rules in numerical integration, namely, the Riemann sums, the trapezoidal rule and the Simpson's rule. We present our research results of these three rules relating to the solving process of our reverse osmosis model. The Simpson's rule is the most accurate, as it has the highest order of accuracy in comparison to the Riemann sums and the trapezoidal rule. Our main point in this research is that the numerical integration has an important role in solving the reverse osmosis model.