On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method
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. Th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2020-06-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amns.2020.2.00008 |
| _version_ | 1818755289145409536 |
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| author | Ikramul Haque B. M. Flora Shajia Afrin |
| author_facet | Ikramul Haque B. M. Flora Shajia Afrin |
| author_sort | Ikramul Haque B. M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T05:36:47Z |
| format | Article |
| id | doaj.art-7af07cb659114ee7878ca9b2ceeb36ab |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-18T05:36:47Z |
| publishDate | 2020-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-7af07cb659114ee7878ca9b2ceeb36ab2022-12-21T21:19:18ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562020-06-016152753610.2478/amns.2020.2.00008On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration methodIkramul Haque B. M.0Flora Shajia Afrin1Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, BangladeshDepartment of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, BangladeshA 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.https://doi.org/10.2478/amns.2020.2.00008extended iteration procedurequadratic oscillatornon-linearitynon-linear oscillations34a3434b99 |
| spellingShingle | Ikramul Haque B. M. Flora Shajia Afrin On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method Applied Mathematics and Nonlinear Sciences extended iteration procedure quadratic oscillator non-linearity non-linear oscillations 34a34 34b99 |
| title | On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method |
| title_full | On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method |
| title_fullStr | On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method |
| title_full_unstemmed | On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method |
| title_short | On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method |
| title_sort | on the analytical approximation of the quadratic non linear oscillator by modified extended iteration method |
| topic | extended iteration procedure quadratic oscillator non-linearity non-linear oscillations 34a34 34b99 |
| url | https://doi.org/10.2478/amns.2020.2.00008 |
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