Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method. (English) Zbl 1264.34067

Summary: 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.


34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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