<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier terms have been used in each step of iterations. The frequencies obtained by this technique show good agreement with the exact frequency. The percentage of error between the exact frequency and our third approximate frequency is as low as 0.001%. There is no algebraic complexity in our calculation, which is why this technique is very easy. The results have been compared with the exact and other existing results, which are both convergent and consistent.</p>
</abstract>

A modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier terms have been used in each step of iterations. The frequencies obtained by this technique show good agreement with the exact frequency. The percentage of error between the exact frequency and our third approximate frequency is as low as 0.001%. There is no algebraic complexity in our calculation, which is why this technique is very easy. The results have been compared with the exact and other existing results, which are both convergent and consistent.

On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

Khulna University of Engineering & Technology

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

A modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier...

On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

Publié en ligne: 15 juin 2020

Pages: 527 - 536

Reçu: 30 sept. 2019

Accepté: 23 déc. 2019

DOI: https://doi.org/10.2478/amns.2020.2.00008

Mots clés
extended iteration procedure, quadratic oscillator, non-linearity, non-linear oscillations

© 2020 B. M. Ikramul Haque et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

Publié en ligne: 15 juin 2020

Pages: 527 - 536

Reçu: 30 sept. 2019

Accepté: 23 déc. 2019

DOI: https://doi.org/10.2478/amns.2020.2.00008

Mots clésextended iteration procedure, quadratic oscillator, non-linearity, non-linear oscillations

© 2020 B. M. Ikramul Haque et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
extended iteration procedure, quadratic oscillator, non-linearity, non-linear oscillations