Accurate Explicit Analytical Solutions of the Duffing-Harmonic Oscillator Equation using Nonlinear Time Transformation - Yamgou'e, Serge Bruno; Nana, Bonaventure; Pelap, FranBeceau (Journal of Applied Nonlinear Dynamics, 2026)
In this paper, we apply a nonlinear time transformation to find accurate analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the restoring force. The transformation considered here has the interesting and useful feature that it leads to fully explicit solutions, in contrast to most such transformations. Its combination with the single term harmonic balance is found to be equivalent to the cubication method. The accuracy of the results can be improved by using the Newton linearization technique when looking for an-harmonic approximate solutions. It is observed that this process not only increases the accuracy of the solutions, but it can also enlarge the range of validity of the approximations in the space of parameters as compared to the method of cubication.