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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 645726, 12 pages
Research Article

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

1Higher Colleges of Technology, Abu Dhabi Men’s College, P.O. Box 25035, Abu Dhabi, UAE
2Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico
3National Institute for Astrophysics, Optics, and Electronics, Luis Enrique Erro No. 1, Santa Maria 72840 Tonantzintla, PUE, Mexico

Received 19 May 2014; Revised 19 August 2014; Accepted 1 September 2014; Published 15 September 2014

Academic Editor: Carlo Piccardi

Copyright © 2014 Brahim Benhammouda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents the application of the differential transform method (DTM) to the model of pollution for a system of three lakes interconnected by channels. Three input models (periodic, exponentially decaying, and linear) are solved to show that DTM can provide analytical solutions of pollution model in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful strategy to extend the domain of convergence of the approximate solutions. The Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant (RKF45) numerical solution of the lakes system problem is used as a reference to compare with the analytical approximations showing the high accuracy of the results. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend of a perturbation parameter.