Application of He’s Variational Iterative Method for Solving Thin Film Flow Problem Arising in Non-Newtonian Fluid Mechanics

Abdul M. Siddiqui, Ali A. Farooq, Tahira Haroon, Muhammad A. Rana, Bruce S. Babcock

COMSATS Institute of Information Technology, Abbottabad, Pakistan.
Department of Basic Sciences, Sector I-14, Riphah International University, Islamabad, Pakistan.
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan.
Department of Mathematics, York Campus, Pennsylvania State University, University Park, USA.

DOI: 10.4236/wjm.2012.23016                

Abstract

In this paper, He’s variational iteration method is successfully employed to solve a nonlinear boundary value problem arising in the study of thin film flow of a third grade fluid down an inclined plane. For comparison, the same problem is solved by the Adomian decomposition method. The results show that the difference between the two solutions is negligible. The conclusion is that this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear boundary value problems. Furthermore, the variational iteration method has an advantage over the decomposition method in that it solves the nonlinear problems without using the Adomian polynomials.

Keywords

Thin Film Flow; Third Grade Fluid; Nonlinear Boundary Value Problem; Variational Iteration Method; Adomian Decomposition Method

Conflicts of Interest

The authors declare no conflicts of interest.

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