#### Authors:

M. M. Ayub Hossain,B. M. Ikramul Haque,#### DOI NO:

https://doi.org/10.26782/jmcms.2021.08.00001#### Keywords:

Extended iteration procedure,Inverse truly nonlinear oscillator,Nonlinearity,Nonlinear oscillations,Fourier series,#### Abstract

*The inverse truly nonlinear oscillator is the most applied in the field of computer science, information technology, physics, electrical engineering, and mechanical engineering. The solution of the inverse truly nonlinear oscillator has been obtained by modified Mickens’ extended iteration procedure. To determine the solution of the oscillator a special type of Fourier series has been used. The iterated solutions are convergent as the second, third, and fourth approximate frequencies of the oscillator show a good concurrence with the exact result. Some researchers presented the solutions of the same oscillator by applying different methods. We have compared the obtained results with some previously published results. Some of their techniques diverge at higher-order stages but the present technique is convergent there. The method is mainly illustrated in the strongly nonlinear inverse oscillator, but it can be widely applicable in other problems arising from nonlinear sciences and engineering.*

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