The simplest approach to solving the cubic nonlinear jerk oscillator with the non-perturbative method

Mathematics and its applications try to make available a simple and accurate approach to handle nonlinear equations. The present paper investigates for the first time the application of the linearizing method to determine both the approximate frequency and displacement amplitude for the third-order differential equations. The main merit of the linearized method is a collection of simplicity and accuracy for the solution of high-order nonlinear conservative or non-conservative oscillators. The current work sheds light on the approximate proposition to the damped third-order nonlinear differential equations. The fast estimated solution is simulated to the accurate solution gained through the numerical methods. It is significant to conclude that the non-perturbative method considered here is simpler and easier to apply than the other perturbation methods. This paper enriches some existing literature.

Automated summary

This paper investigates the application of the linearizing method to determine both the approximate frequency and displacement amplitude for third-order differential equations. The results show that the non-perturbative method considered here is simpler and easier to apply than other perturbation methods.