An Analytic Investigation of the Quadratic Nonlinear Oscillator by an Iteration Method
B. M. Ikramul Haque *
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.
*Author to whom correspondence should be addressed.
Abstract
A modified approximate analytic solution of the quadratic nonlinear oscillator “ ẍ + x2 sgn(x) =0 ” 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 our technique shows a good agreement with the exact frequency. The percentage of error between exact frequency and our fourth approximate frequency is as low as 0.00003%.
Keywords: Nonlinear oscillator, quadratic nonlinear oscillator, iteration method.