On the numerical approximations and simulations of damped and undamped Duffing oscillators

Abstract

The Duffing oscillator (damped or undamped) is one of the most significant and classical 
nonlinear ordinary differential equations in view of its diverse applications in science and 
engineering. The Duffing oscillator is an equation that has a cubic stiffness term regard
less of the type of damping or excitation. Over the years, different methods have been 
developed for the solution of Duffing oscillators. In this paper, a new method is derived 
for the approximation and simulation of damped and undamped Duffing oscillators. In 
deriving the method, a power series was employed as a basis function by carrying out the 
integration within one-step interval. The results obtained clearly showed that the method 
derived is efficient in approximating Duffing oscillators. The phase plots generated equally 
show that the method is computationally reliable in simulating Duffing oscillators. The 
paper has further analyzed some properties of the method. The outcome of the analysis 
shows that the method derived is consistent, convergent, and zero-stable.