"Quintication" method to obtain approximate analytical solutions of non-linear oscillators

In this paper we propose a new approach to replace nonlinear ordinary differential equations by approximate cubic-quintic Duffing oscillators in which its coefficients depend on the initial amplitude of oscillation. It is shown that this procedure leads to angular frequency values with relative errors that are lower than those found by previously developed approximate solutions.

[1]  Inmaculada Pascual,et al.  Cubication of conservative nonlinear oscillators , 2009 .

[2]  A. Elías-Zúñiga,et al.  Accurate Solutions of Conservative Nonlinear Oscillators by the Enhanced Cubication Method , 2013 .

[3]  Augusto Beléndez,et al.  An accurate closed-form approximate solution for the quintic Duffing oscillator equation , 2010, Math. Comput. Model..

[4]  M. Febbo,et al.  A finite extensibility nonlinear oscillator , 2011, Appl. Math. Comput..

[6]  A. Elías-Zúñiga.  Exact solution of the cubic-quintic Duffing oscillator , 2013 .

[7]  A weighted mean square method of linearization in non-linear oscillations , 1971 .

[8]  S. B. Yuste,et al.  A weighted mean-square method of ``cubication'' for non-linear oscillators , 1989 .

[10]  Wilfred D. Iwan.  On defining equivalent systems for certain ordinary non-linear differential equations , 1969 .

[11]  Augusto Beléndez,et al.  An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method , 2009 .

[12]  S. K. Lai,et al.  Application of a generalized Senator-Bapat perturbation technique to nonlinear dynamical systems with an irrational restoring force , 2010, Comput. Math. Appl..

[13]  S. B. Yuste,et al.  “Cubication” of non-linear oscillators using the principle of harmonic balance , 1992 .

[14]  Alexei G. Ershov,et al.  Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion , 2005, Reliab. Comput..

[15]  Inmaculada Pascual,et al.  Comments on 'A finite extensibility nonlinear oscillator' , 2012, Appl. Math. Comput..