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

Discrete Dynamics in Nature and Society. 2014;2014 DOI 10.1155/2014/645726


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Journal Title: Discrete Dynamics in Nature and Society

ISSN: 1026-0226 (Print); 1607-887X (Online)

Publisher: Hindawi Limited

LCC Subject Category: Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML



Brahim Benhammouda (Higher Colleges of Technology, Abu Dhabi Men’s College, P.O. Box 25035, Abu Dhabi, UAE)

Hector Vazquez-Leal (Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico)

Luis Hernandez-Martinez (National Institute for Astrophysics, Optics, and Electronics, Luis Enrique Erro No. 1, Santa Maria 72840 Tonantzintla, PUE, Mexico)


Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 23 weeks


Abstract | Full Text

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.