Solution to a Damped Duffing Equation Using He’s Frequency Approach
In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function c...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2022/5009722 |
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| author | Alvaro H. S. Salas Gilder-Cieza Altamirano Manuel Sánchez-Chero |
| author_facet | Alvaro H. S. Salas Gilder-Cieza Altamirano Manuel Sánchez-Chero |
| author_sort | Alvaro H. S. Salas |
| collection | DOAJ |
| description | In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques. |
| format | Article |
| id | doaj-art-9928149c19084ca380357dbe7e9eb0aa |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-9928149c19084ca380357dbe7e9eb0aa2025-08-20T03:37:03ZengWileyThe Scientific World Journal1537-744X2022-01-01202210.1155/2022/5009722Solution to a Damped Duffing Equation Using He’s Frequency ApproachAlvaro H. S. Salas0Gilder-Cieza Altamirano1Manuel Sánchez-Chero2Universidad Nacional de ColombiaUniversidad Nacional Autónoma de ChotaUniversidad Nacional de FronteraIn this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.http://dx.doi.org/10.1155/2022/5009722 |
| spellingShingle | Alvaro H. S. Salas Gilder-Cieza Altamirano Manuel Sánchez-Chero Solution to a Damped Duffing Equation Using He’s Frequency Approach The Scientific World Journal |
| title | Solution to a Damped Duffing Equation Using He’s Frequency Approach |
| title_full | Solution to a Damped Duffing Equation Using He’s Frequency Approach |
| title_fullStr | Solution to a Damped Duffing Equation Using He’s Frequency Approach |
| title_full_unstemmed | Solution to a Damped Duffing Equation Using He’s Frequency Approach |
| title_short | Solution to a Damped Duffing Equation Using He’s Frequency Approach |
| title_sort | solution to a damped duffing equation using he s frequency approach |
| url | http://dx.doi.org/10.1155/2022/5009722 |
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