(untitled) (Journal of Pure and Applied Sciences (Science Forum), 2026)
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.