Approximate Solution of Nonlinear Duffing Oscillator Using Taylor Expansion

The Duffing oscillator is a common model for nonlinear phenomena in science and engineering. Its mathematical model is a second order differential equation with nonlinear spring force used to describe the motion of a damped oscillator with a more complicated potential than in simple harmonic motion. In the present paper, the Duffing oscillator equation is solved using a new simple technique based on Taylor theory. The Duffing oscillator equation is solved with different values of initial conditions and damping. The solution results are compared with Runge-Kutta 4 th order numerical solution method to investigate the accuracy and reliability of the suggested technique. Results show an excellent agreement between the proposed technique and the Runge-Kutta method.