Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the pattern formation in liquid drops

Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the... Purpose – Rosenau‐Hyman equation was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops. Also, this equation has important roles in the modelling of various problems in physics and engineering. The purpose of this paper is to present the solution of Rosenau‐Hyman equation. Design/methodology/approach – This paper aims to present the solution of the Rosenau‐Hyman equation by means of semi‐analytical approaches which are based on the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM). Findings – These techniques reduce the volume of calculations by not requiring discretization of the variables, linearization or small perturbations. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. These results reveal that the proposed methods are very effective and simple to perform. Originality/value – Efficient techniques are developed to find the solution of an important equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the pattern formation in liquid drops

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Publisher
Emerald Publishing
Copyright
Copyright © 2012 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/09615531211244916
Publisher site
See Article on Publisher Site

Abstract

Purpose – Rosenau‐Hyman equation was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops. Also, this equation has important roles in the modelling of various problems in physics and engineering. The purpose of this paper is to present the solution of Rosenau‐Hyman equation. Design/methodology/approach – This paper aims to present the solution of the Rosenau‐Hyman equation by means of semi‐analytical approaches which are based on the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM). Findings – These techniques reduce the volume of calculations by not requiring discretization of the variables, linearization or small perturbations. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. These results reveal that the proposed methods are very effective and simple to perform. Originality/value – Efficient techniques are developed to find the solution of an important equation.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Aug 3, 2012

Keywords: Homotopy perturbation method (HPM); Variational iteration method (VIM); Adomian decomposition method (ADM); Rosenau‐Hyman equation; Liquids; Variational techniques

References

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