### Mathematical modelling and application of reduced differential transform method for river pollution

Manan A. Maisuria, Priti V. Tandel

#### Abstract

This paper presents the mathematical model of pollutant transport in a river. To effectively find the analytical solution of the advectiondiffusion equation under various forms of suitable initial conditions, the reduced differential transform method (RDTM) is used. Three different initial concentration function cases, including rational, exponential, and power, are analyzed for the present model. A 2D and 3D visual comparison of the solutions obtained for each case is also shown. This article discusses the sufficient condition for convergence of the reduced differential transform approach to solving non-linear differential equations. The convergence results for the concentration functions in each case are briefly described. The present method is highly effective and more efficient in solving real-world problems. For all cases, the amount of phosphate pollutant concentration at various distances and time levels has been examined using numerical and graphical representations. While analyzing actual world problems, the current study demonstrates its effectiveness.

#### Keywords

Pollutant transport equation; Reduced differential transform method; Convergence; River pollution

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DOI: http://dx.doi.org/10.23755/rm.v47i0.955

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