4.7 Article

New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM

Journal

COMPUTER PHYSICS COMMUNICATIONS
Volume 180, Issue 9, Pages 1539-1544

Publisher

ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2009.04.009

Keywords

Differential transform method (DTM); Burgers' equation; Nonlinear differential equation; Homotopy analysis method (HAM); Fin

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In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM {M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499} and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions. (C) 2009 Elsevier B.V, All rights reserved.

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