Composite group of explicit Runge-Kutta methods
In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of funct...
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| Main Authors: | , , |
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| 格式: | Conference or Workshop Item |
| 語言: | English |
| 出版: |
AIP Publishing
2016
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| 在線閱讀: | http://psasir.upm.edu.my/id/eprint/57159/1/Composite%20group%20of%20explicit%20Runge-Kutta%20methods.pdf http://psasir.upm.edu.my/id/eprint/57159/ http://aip.scitation.org/doi/abs/10.1063/1.4952537 |
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| 總結: | In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method. |
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