Mickens Iteration Like Method for Approximate Solutions of the Inverse Cubic Truly Nonlinear Oscillator
B. M. Ikramul Haque *
Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.
Md. Bayezid Bostami
Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.
M. M. Ayub Hossain
Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.
Md. Rakib Hossain
Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.
Md. Mominur Rahman
Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
A new technique of the Mickens iterative method has been presented to obtain approximate analytic solutions of the Inverse Cubic Truly Nonlinear Oscillator. In this paper, we have used Fourier series and utilized truncated terms in each steps of iteration. The method is illustrated by an example and the solutions obtained by this method agree nicely with the exact frequency. Also the solutions give more accurate result than other existing results and the method is convergent.
Keywords: Iterative method, nonlinear oscillators, inverse cubic oscillator, frequency, fourier series.