A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure
B. M. Ikramul Haque *
Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh.
M. M. Ayub Hossain
Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh and Department of Non-Technical, Shahid Abdur Rab Serniabat Textile Engineering College, Barishal, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
A modified solution of the nonlinear singular oscillator has been obtained based on the extended iteration procedure. We have used an appropriate truncation of the obtained Fourier series in each step of iterations to determine the approximate analytic solution of the oscillator. The third approximate frequency of the nonlinear singular oscillator shows a good agreement with its exact values. Earlier different authors presented the analytic solution of the oscillator by using various types of methods. We have compared the results obtained by the modified technique with some of the existing results. We see that some of their techniques deviate from higher-order approximations and the present technique performs comparatively better. The rate of change of percentage of error of the presented modified solution shows the validity of convergence.
Keywords: Extended iteration procedure, singular oscillator, nonlinearity, nonlinear oscillations.