A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators
In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/236281 |
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| _version_ | 1832560505143689216 |
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| author | Zhaoxia Chen Xiong You Xin Shu Mei Zhang |
| author_facet | Zhaoxia Chen Xiong You Xin Shu Mei Zhang |
| author_sort | Zhaoxia Chen |
| collection | DOAJ |
| description | In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. The linear stability and phase properties of the new methods are examined. The results of numerical experiments on physical and biological problems show the robustness and competence of the new methods compared to some highly efficient integrators in the literature. |
| format | Article |
| id | doaj-art-17762d8f581e428196f4a587b6ed1091 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-17762d8f581e428196f4a587b6ed10912025-02-03T01:27:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/236281236281A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for OscillatorsZhaoxia Chen0Xiong You1Xin Shu2Mei Zhang3Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, ChinaDepartment of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, ChinaDepartment of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, ChinaDepartment of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, ChinaIn order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. The linear stability and phase properties of the new methods are examined. The results of numerical experiments on physical and biological problems show the robustness and competence of the new methods compared to some highly efficient integrators in the literature.http://dx.doi.org/10.1155/2012/236281 |
| spellingShingle | Zhaoxia Chen Xiong You Xin Shu Mei Zhang A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators Journal of Applied Mathematics |
| title | A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators |
| title_full | A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators |
| title_fullStr | A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators |
| title_full_unstemmed | A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators |
| title_short | A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators |
| title_sort | new family of phase fitted and amplification fitted runge kutta type methods for oscillators |
| url | http://dx.doi.org/10.1155/2012/236281 |
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