Haque’s approach with mickens’ iteration method to find a modified analytical solution of nonlinear jerk oscillator containing displacement time velocity and time acceleration

Haque’s approach with Mickens’ iteration method has been used to obtain the modified analytical solutions of the nonlinear jerk oscillator, including displacement time velocity and acceleration. The jerk oscillator represents the features of chaotic behavior in numerous nonlinear phenomena, cosmological analysis, kinematical physics, pendulum analysis, etc., such as electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. In this paper, we have used different harmonic terms for different iterative stages using the truncated Fourier series. A comparison is made between the iteration method, the improved harmonic balance method, and the homotopy perturbation method. After comparison, the suggested approach has been shown to be more precise, efficient, simple, and easy to use. Furthermore, there was remarkable accuracy in the comparison between the numerical results and the generated analytical solutions. For the third approximate period, the maximum percentage error is 0.014.