Improvement of Analytical Solution to the Inverse Truly Nonlinear Oscillator by Extended Iterative Method

  • B. M. Ikramul HaqueEmail author
  • Md. Asifuzzaman
  • M. Kamrul Hasan
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)


A new approach to the Mickens extended iteration method has been presented to obtain approximate analytic solutions for nonlinear oscillatory differential equation. To illustrate the accuracy of the approximate solution of the inverse nonlinear oscillator “\( \ddot{x} + x^{ - 1} = 0 \)”, we have used the Fourier series and utilized indispensable truncated terms in each iterative step. In this article the solution gives more accurate result significantly than other existing methods and shows a good agreement with its exact solution. The percentage of error between exact frequency and our third approximate frequency is very low. We have compared all the results to exact results and other existing results and the method is convergent as well as consistent. Finally, an example is given to show the effectiveness of the approximate solution.


Extended iterative method Inverse truly nonlinear oscillator Analytical solution 

AMS Subject Classification

34A34 34B99 



The authors are grateful to the honorable reviewers’ for their constructive suggestions/comments to improve the quality of this article. The authors are also grateful to Md. Shahinur Alam Sarker, Assistant Professor, Department of Humanities, Khulna University of Engineering & Technology, Khulna-9203, for his assistance to prepare the revised manuscript.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • B. M. Ikramul Haque
    • 1
    Email author
  • Md. Asifuzzaman
    • 1
  • M. Kamrul Hasan
    • 2
  1. 1.Department of MathematicsKhulna University of Engineering & TechnologyKhulnaBangladesh
  2. 2.Department of MathematicsRajshahi University of Engineering & TechnologyRajshahiBangladesh

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