Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method
We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/691614 |
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| _version_ | 1832566183557070848 |
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| author | Berna Bülbül Mehmet Sezer |
| author_facet | Berna Bülbül Mehmet Sezer |
| author_sort | Berna Bülbül |
| collection | DOAJ |
| description | We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems. |
| format | Article |
| id | doaj-art-1f99a97a5cb749918f39aa4e8247b06e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1f99a97a5cb749918f39aa4e8247b06e2025-02-03T01:04:42ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/691614691614Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix MethodBerna Bülbül0Mehmet Sezer1Department of Mathematics, Faculty of Science, Muğla University, 48000 Muğla, TurkeyDepartment of Mathematics, Faculty of Science, Celal Bayar University, 45000 Manisa, TurkeyWe have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.http://dx.doi.org/10.1155/2013/691614 |
| spellingShingle | Berna Bülbül Mehmet Sezer Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method Journal of Applied Mathematics |
| title | Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method |
| title_full | Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method |
| title_fullStr | Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method |
| title_full_unstemmed | Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method |
| title_short | Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method |
| title_sort | numerical solution of duffing equation by using an improved taylor matrix method |
| url | http://dx.doi.org/10.1155/2013/691614 |
| work_keys_str_mv | AT bernabulbul numericalsolutionofduffingequationbyusinganimprovedtaylormatrixmethod AT mehmetsezer numericalsolutionofduffingequationbyusinganimprovedtaylormatrixmethod |