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

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.