Abstract
Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. The main feature of the NIM is that the procedure is very simple, and it does not need to calculate any special type of polynomial or multipliers such as Adomian polynomials and Lagrange’s multipliers. Comparisons with the Adomian decomposition method (ADM) and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the NIM is a powerful alternative for differential equations providing more realistic series solutions that converge very rapidly in real physical problems.
Highlights
Over the years, differential equations are employed by researchers that care about what is going on in the surroundings, for example, one can see the following ref. [1,2,3,4,5,6,7,8,9,10]
Numerous authors used some of the approximate numerical techniques to obtain approximate analytical solutions such as the Bessel matrix method [17], Haar wavelet collocation method [18], Differential Transform method (DTM) [19], Laplace-Padé Differential transform method (LPDTM) [20], and variational iteration method (VIM) [21]
We have presented the new iterative method (NIM) as a useful analytic-numeric tool to solve pollution model for a system of three interconnecting lakes
Summary
Differential equations are employed by researchers that care about what is going on in the surroundings, for example, one can see the following ref. [1,2,3,4,5,6,7,8,9,10]. Several semianalytic methods including the Adomian decomposition method (ADM) [11], homotopy perturbation method (HPM) [12], and variational iteration method (VIM) [13] have been used for solving mathematical models of differential equations. Numerous authors used some of the approximate numerical techniques to obtain approximate analytical solutions such as the Bessel matrix method [17], Haar wavelet collocation method [18], Differential Transform method (DTM) [19], Laplace-Padé Differential transform method (LPDTM) [20], and variational iteration method (VIM) [21] Another prominent semianalytical technique which has been demonstrated to be a lot more straightforward and efficient than the abovementioned methods is called the new iterative method (NIM), first proposed by Varsha Daftardar-Gejji and Jafari [22]. The NIM motivates us to solve the lake pollution systems
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