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Item Approximate Analytic Solutions of the Nonlinear Cubic Oscillator by Iterative Method(Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh, 2016-11) Rahman, Md. Mominur; Haque, Dr. B. M. IkramulA modified approximate analytic solution of the cubic nonlinear oscillator “ẍ + x3 = 0" has been obtained based on an iteration method. 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. The modified technique accelerates the rapid convergence of the solution, reduces the error solution and increases the validity range.Item Approximate Analytic Solutions of the Inverse Cubic Truly Nonlinear Oscillator by Iterative Method(Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh., 2016-01) Bostami, Md. Bayezid; Haque, Dr. B. M. IkramulAn analytical technique has been developed based on an iteration method to determine higher-order approximate periodic solutions for nonlinear oscillatory differential equations. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of large oscillations. A new technique based on the Mickens iterative method has been presented to obtain approximate analytic solutions of the Inverse Cubic Truly Nonlinear Oscillator. In this thesis, we have adopted the method of Fourier series and utilized truncated terms in each steps of iteration. The solutions obtained by this method nicely matched with the exact frequency. Also the obtained solutions are much more accurate than other existing results and the method is convergent and consistent.