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Research Article Open access CC BY 4.0

On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method

B. M. Ikramul Haque, A. K. M. Selim Reza, Md. Mominur Rahman

Journal of Advances in Mathematics and Computer Science · pp. 1–9 · Published 29 Jul 2019

10.9734/jamcs/2019/v33i330177

Abstract

A modified approximate analytic solution of the cubic nonlinear oscillator “ ” has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by this technique show a good agreement with the exact frequency. The percentage of error between exact frequency and our fifth approximate frequency is as low as 0.009%. The calculation with this technique is very easy. This easily-calculated modified technique accelerates the rapid convergence, reduces the error and increases the validity range of the solution.

Iteration procedure cubic oscillator nonlinearity nonlinear oscillations.

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Cited by 21

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

Md. Ishaque Ali, B. M. Ikramul Haque, M. M. Ayub Hossain · Journal of Umm Al-Qura University for Applied Sciences · 2024

PERIODIC SOLUTION OF THE NONLINEARJERK OSCILLATOR CONTAINING VELOCITY TIMES ACCELERATION-SQUARED: ANITERATION APPROACH

B. M. IkramulHaque · JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES · 2020

On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

B. M. Ikramul Haque, Shajia Afrin Flora · Applied Mathematics and Nonlinear Sciences · 2020

Explaining the singular oscillator: physical considerations and mechanical analogies

Stylianos Vasileios Kontomaris, Anna Malamou · European Journal of Physics · 2025

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