An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure
The cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/7819209 |
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| author | B. M. Ikramul Haque M. M. Ayub Hossain |
| author_facet | B. M. Ikramul Haque M. M. Ayub Hossain |
| author_sort | B. M. Ikramul Haque |
| collection | DOAJ |
| description | The cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of elastic force, structural dynamics, and elliptic curve cryptography. In this paper, we have applied modified Mickens extended iteration method to solve the cube-root truly nonlinear oscillator, the inverse cube-root truly nonlinear oscillator, and the equation of pendulum. Comparison is made among iteration method, harmonic balance method, He’s amplitude-frequency formulation, He’s homotopy perturbation method, improved harmonic balance method, and homotopy perturbation method. After comparison, we analyze that modified Mickens extended iteration method is more accurate, effective, easy, and straightforward. Also, the comparison of the obtained analytical solutions with the numerical results represented an extraordinary accuracy. The percentage error for the fourth approximate frequency of cube-root truly nonlinear oscillator is 0.006 and the percentage error for the fourth approximate frequency of inverse cube-root truly nonlinear oscillator is 0.12. |
| format | Article |
| id | doaj-art-5c566f3ed5b3473495e4961cd722dccb |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-5c566f3ed5b3473495e4961cd722dccb2025-08-20T03:34:13ZengWileyInternational Journal of Differential Equations1687-96512021-01-01202110.1155/2021/7819209An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration ProcedureB. M. Ikramul Haque0M. M. Ayub Hossain1Department of MathematicsDepartment of MathematicsThe cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of elastic force, structural dynamics, and elliptic curve cryptography. In this paper, we have applied modified Mickens extended iteration method to solve the cube-root truly nonlinear oscillator, the inverse cube-root truly nonlinear oscillator, and the equation of pendulum. Comparison is made among iteration method, harmonic balance method, He’s amplitude-frequency formulation, He’s homotopy perturbation method, improved harmonic balance method, and homotopy perturbation method. After comparison, we analyze that modified Mickens extended iteration method is more accurate, effective, easy, and straightforward. Also, the comparison of the obtained analytical solutions with the numerical results represented an extraordinary accuracy. The percentage error for the fourth approximate frequency of cube-root truly nonlinear oscillator is 0.006 and the percentage error for the fourth approximate frequency of inverse cube-root truly nonlinear oscillator is 0.12.http://dx.doi.org/10.1155/2021/7819209 |
| spellingShingle | B. M. Ikramul Haque M. M. Ayub Hossain An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure International Journal of Differential Equations |
| title | An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure |
| title_full | An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure |
| title_fullStr | An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure |
| title_full_unstemmed | An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure |
| title_short | An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure |
| title_sort | effective solution of the cube root truly nonlinear oscillator extended iteration procedure |
| url | http://dx.doi.org/10.1155/2021/7819209 |
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