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Research Article Open access CC BY 4.0

A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure

B. M. Ikramul Haque, M. M. Ayub Hossain

Journal of Advances in Mathematics and Computer Science · pp. 1–9 · Published 26 Oct 2019

10.9734/jamcs/2019/v34i3-430204

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.

Extended iteration procedure singular oscillator nonlinearity nonlinear oscillations.

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