VIM for Solving the Pollution Problem of a System of Lakes

Abstract

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. In this paper the pollution problem of three lakes with interconnecting channels has been studied. The variational iteration method has been applied to compute an approximate solution of the system of differential equations, governing on the problem. Three different types of input models: sinusoidal, impulse, and step will be considered for monitoring the pollution in the lakes. The results are compared with those obtained by Adomian decomposition method. This comparison reveals that the variational iteration method is easier to be implemented.

A New Technique for Solving Fractional Order Systems: Hermite Collocation Method

“…In conclusion, writing these coefficients into: In [30], the authors have modeled the pollutant problem in a lake which connected by channels by the following fractional order system (see Figure 3), 13 31 21 1 3 1 1 3 1 1 32 21 2 1 2 1 2 31 32 13 3 1 2 3 1 2 3 then, it requires that 1 t = . As a result, we can choose 3 N = .…”

“…shows the HCM solution of the system, Equation(30).Figure 2(a)) shows the Differential Transform solution and Figure 2(b)) Adomian Decomposition solution of the same system. Example 6.2.…”

Modified Differential Transform Method for Solving the Model of Pollution for a System of Lakes

“…For the solution procedure with LPDTM, we take the differential transform of (36) and system (35), respectively, to get…”

“…Therefore, in this paper, we present the application of a hybrid technique combining DTM, Laplace transform, and Padé approximant [28] to find approximate analytical solutions for a pollution model [29][30][31][32][33][34]. The aim of the model is to describe the pollution of a system of three lakes [35][36][37][38][39] as depicted in Figure 1. Each lake is considered to be as large compartment and the interconnecting channels as pipes between the compartments with given flow directions.…”

Penggunaan Metode Homotopi Untuk Menyelesaikan Model Aliran Polutan Di Tiga Danau Yang Saling Terhubung

“…Beberapa penelitian difokuskan pada penemuan metode pendekatan analitik untuk memeroleh penyelesaian dari masalah yang dimodelkan dalam suatu persamaan diferensial. Beberapa metode yang telah digunakan untuk menyelesaikan model laju alir polutan pada tiga danau dengan saluran yang saling terhubung adalah metode aproksimasi Pade' (Merdan 2008), metode perturbasi (Merdan 2009), metode modifikasi transformasi diferensial (Merdan 2010), dan metode iterasi variasi (Biazar et al 2010).…”