ADEQUATE SOLUTIONS OF JERK OSCILLATORS CONTAINING VELOCITY TIMES ACCELERATION-SQUARED: HAQUE’S APPROACH WITH MICKENS’ ITERATION METHOD

Authors:

Md. Ishaque Ali,B M Ikramul Haque,M. M. Ayub Hossain,

DOI NO:

https://doi.org/10.26782/jmcms.2023.05.00001

Keywords:

Jerk equation,Truncated Fourier series,Newton’s method,Angular frequency,Haque’s Approach with Mickens’ Iteration Method,Autonomous,Chaotic solutions,

Abstract

Haque’s Approach with Mickens’ Iteration Method is used to find the exact analytic solution of the nonlinear equation involving velocity times acceleration squared. A truncated Fourier series is used in different rhythms with different repetition steps. Our results are very close to the exact results and our results are comparatively closer to the exact results than others. Our solution method is obtained around the second-order angular frequency using Newton's method. For some third-order (jerk) differential equations with cubic nonlinearities and nonlinear second-order differential equations; Mickens' iteration method is used to determine the exact analytical approximate periodic solution. A numerical experiment of general differential equations with third-order, one-dimensional, autonomous, quadratic, and cubic nonlinearity has uncovered several algebraically simple equations involving the shaking of time-dependent acceleration that contain chaotic solutions.

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