Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method

Authors:
Reza Abazari;A. Borhanifar
Affiliations:
Department of Mathematics, Islamic Azad University-Ardabil Branch, P.O. Box 56169-54184, Ardabil, Iran;Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, the Differential Transformation Method (DTM) is employed to obtain the numerical/analytical solutions of the Burgers and coupled Burgers equations. We begin by showing how the differential transformation method applies to the linear and nonlinear parts of any PDE and give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. We also compare it against three famous methods, namely the homotopy perturbation method, the homotopy analysis method and the variational iteration method. These results show that the technique introduced here is accurate and easy to apply.