Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs
A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solvin...
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| Main Authors: | , , , |
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| 格式: | Article |
| 語言: | English |
| 出版: |
Hikari Ltd
2018
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| 主題: | |
| 在線閱讀: | http://eprints.uthm.edu.my/5538/1/AJ%202018%20%28567%29.pdf http://eprints.uthm.edu.my/5538/ http://dx.doi.org/10.12988/ams.2014.46403 |
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| 總結: | A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solving a standard set of test problems, which then reduced to first-order system when solved using Runge-Kutta (RK) method and comparison are made with existing RK method with same order using variable step-size. The results clearly showed the advantage and the efficiency of the new method. |
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