Open AccessAn efficient new iterative method for oscillator differential equation
Author(s) -
Yasir Khan,
H. Vázquez-Leal,
Naeem Faraz
Publication year - 2012
Publication title -
scientia iranica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.299
H-Index - 51
eISSN - 2345-3605
pISSN - 1026-3098
DOI - 10.1016/j.scient.2012.10.018
Subject(s) - van der pol oscillator , convergent series , duffing equation , linearization , mathematics , homotopy analysis method , perturbation (astronomy) , nonlinear system , homotopy perturbation method , poincaré–lindstedt method , exact solutions in general relativity , simple (philosophy) , mathematical analysis , iterative method , differential equation , homotopy , mathematical optimization , physics , singular perturbation , power series , philosophy , epistemology , quantum mechanics , pure mathematics
In this paper, a Van der Pol–Duffing oscillator is studied. Governing equations are solved by using a newly proposed method, namely; the “Homotopy Perturbation Transform Method” (HPTM). The beauty of the paper is error analysis between the exact solutions, approximate solutions and numerical solutions, which shows that our approximate solutions converge very rapidly to the exact solutions. HPTM is not limited to the small parameter, such as in the classical perturbation method. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. Results indicate that this technique is very effective and simple for solving nonlinear oscillatory systems. The solution procedure confirms that this method can be easily extended to other kinds of nonlinear oscillator equations