On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method
B. M. Ikramul Haque *
Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.
A. K. M. Selim Reza
Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.
Md. Mominur Rahman
Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.
*Author to whom correspondence should be addressed.
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.
Keywords: Iteration procedure, cubic oscillator, nonlinearity, nonlinear oscillations.