Homotopy perturbation method for strongly nonlinear oscillators

This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to elucidate the solving process step by step, and a nonlinear frequency-amplitude relationship is obtained with a relative error of 0.91% when the amplitude tends to infinity, the solution morphology is also discussed, and the zero-th approximate solution is enough for conservative nonlinear oscillators, while the accuracy of the frequency can be improved if the iteration continues. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to illustrate the solving process step by step. A nonlinear frequency-amplitude relationship with a relative error of 0.91% is obtained, and the solution morphology is discussed along with the improvement of accuracy.