Open AccessAn analytical coupled homotopy-variational approach for solving strongly nonlinear differential equation
Author(s) -
Gamal M. Ismail
Publication year - 2017
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2017.07.006
Subject(s) - mathematics , correctness , nonlinear system , homotopy analysis method , homotopy perturbation method , inertia , oscillation (cell signaling) , range (aeronautics) , homotopy , amplitude , linearity , work (physics) , exact solutions in general relativity , mathematical analysis , differential equation , algorithm , classical mechanics , physics , pure mathematics , materials science , quantum mechanics , biology , composite material , genetics , thermodynamics
In the present paper, a novel technique combining the homotopy concept with variational formula has been presented to find accurate analytical solution for nonlinear differential equation with inertia and static non-linearity. The obtained results are compared with other analytical and exact solutions to confirm the excellent accuracy and correctness of the approximate analytical technique. The results of the present paper are valid for large amplitudes of oscillation; also the approximate solutions give excellent result than other methods. We concluded that the first order approximation obtained in current work are almost the same with exact solutions, also works very well for the whole range of initial amplitudes. Keywords: Analytical solution, Strongly nonlinear oscillator, Homotopy perturbation method, Variational approach, MSC: 34A34, 34C15, 34C25, 35L65, 37N30, 74S2