Novel solution for acceleration motion of a vertically falling non-spherical particle by VIM–Padé approximant

In this paper, the acceleration motion of a vertically falling non-spherical particle in incompressible Newtonian media was investigated. The velocity and acceleration were carried out using analytical solution techniques i.e., the variational iteration method (VIM) and a Padé approximant. The results were also compared with VIM and the established fourth order Runge–Kutta method in order to verify the accuracy of the proposed method. It was shown that this method can lead into more accurate results compared with VIM.

Graphical abstractVIM–Padé approximant, VIM (3rd iteration) and numerical solutions of the 3rd equation. This figure depicts the velocity versus time for the three methods. It is observed that the VIM–Padé approximant solution is more accurate than VIM [6].Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► The acceleration motion of a falling non-spherical particle is investigated. ► The velocity analysis is carried out by using a VIM–Padé technique. ► It is found that this method can achieve more suitable results compared with VIM.