The damping Helmholtz-Rayleigh-Duffing oscillator with the non-perturbative approach

The present study suggests a very simple, effective new method to study the damping quadratic-cubic nonlinear oscillation in physical phenomena such as fluid, solid-state physics, optics, plasma physics, dispersion, and convection systems with no perturbation. The damping nonlinear oscillation is converted to its equivalent linear oscillation. The exact solution of the corresponding linear oscillation is verified by the first-order homotopy perturbation method which shows an exact agreement. Stability conditions are imposed from the frequency formula. The accuracy of the proposed approach has shown that the approximate analytical solutions are in excellent agreement with the corresponding exact solutions. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

The present study proposes a simple and effective new method to study damping quadratic-cubic nonlinear oscillation without perturbation, by converting it into an equivalent linear oscillation. The accuracy and stability of the method are demonstrated through the verification of exact solutions.