Singular perturbation

Pure mathematics

Mathematics

Homotopy perturbation method

Duffing equation

Homotopy analysis method

Quantum mechanics

Poincaré–Lindstedt method

Perturbation (astronomy)

Applied mathematics

Mathematical analysis

Homotopy

Physics

Nonlinear system

Journal of low frequency noise, vibration and active control

The enhanced perturbation method is used to improve a governing equation to a higher order, followed by the classic perturbation method. This paper adopts the basic idea of the method to construct a homotopy equation with a higher order. The results show that this modification of the homotopy perturbation method leads to a very high accuracy of the obtained solution. Its solution process is elucidated by using Duffing oscillator as an example, and the obtained frequency is valid for all amplitudes from an extremely small value to infinity with a maximal error of 3.34%. The main merit of this higher order homotopy perturbation method is that the obtained frequency is valid for the whole solution domain.

Homotopy perturbation method coupled with the enhanced perturbation method