Open AccessNinety years of Duffing’s equation
Author(s) -
L. Cvetićanin
Publication year - 2013
Publication title -
theoretical and applied mechanics/theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam1301049c
Subject(s) - duffing equation , homotopy perturbation method , elliptic function , mathematics , elliptic curve , exact solutions in general relativity , generalization , mathematical analysis , homotopy , physics , pure mathematics , nonlinear system , quantum mechanics
In the paper the origin of the so named ‘Duffing’s equation’ is shown. The author’s generalization of the equation, her published papers dealing with Duffing’s equation and some of the solution methods are presented. Three characteristic approximate solution procedures based on the exact solution of the strong cubic Duffing’s equation are shown. Using the Jacobi elliptic functions the elliptic-Krylov-Bogolubov (EKB), the homotopy perturbation and the elliptic-Galerkin (EG) methods are described. The methods are compared. The advantages and the disadvantages of the methods are discussed