Approximate solution for the duffing-harmonic oscillator by the enhanced cubication method

The cubication and the equivalent nonlinearization methods are used to replace the original Duffing-harmonic oscillator by an approximate Duffing equation in which the coefficients for the linear and cubic terms depend on the initial oscillation amplitude. It is shown that this procedure leads to angular frequency values with a maximum relative error of 0.055. This value is 21 lower than the relative errors attained by previously developed approximate solutions. © 2012 Alex Elías-Zúiga et al