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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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57159/1/Composite%20group%20of%20explicit%20Runge-Kutta%20methods.pdf |
| _version_ | 1796976634951106560 |
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| author | Abd Hamid, Fatin Nadiah Rabiei, Faranak Ismail, Fudziah |
| author_facet | Abd Hamid, Fatin Nadiah Rabiei, Faranak Ismail, Fudziah |
| author_sort | Abd Hamid, Fatin Nadiah |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T09:28:33Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57159 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:33Z |
| publishDate | 2016 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | upm.eprints-571592017-09-08T05:20:56Z http://psasir.upm.edu.my/id/eprint/57159/ Composite group of explicit Runge-Kutta methods Abd Hamid, Fatin Nadiah Rabiei, Faranak Ismail, Fudziah 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. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57159/1/Composite%20group%20of%20explicit%20Runge-Kutta%20methods.pdf Abd Hamid, Fatin Nadiah and Rabiei, Faranak and Ismail, Fudziah (2016) Composite group of explicit Runge-Kutta methods. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. (pp. 1-7). http://aip.scitation.org/doi/abs/10.1063/1.4952537 10.1063/1.4952537 |
| spellingShingle | Abd Hamid, Fatin Nadiah Rabiei, Faranak Ismail, Fudziah Composite group of explicit Runge-Kutta methods |
| title | Composite group of explicit Runge-Kutta methods |
| title_full | Composite group of explicit Runge-Kutta methods |
| title_fullStr | Composite group of explicit Runge-Kutta methods |
| title_full_unstemmed | Composite group of explicit Runge-Kutta methods |
| title_short | Composite group of explicit Runge-Kutta methods |
| title_sort | composite group of explicit runge kutta methods |
| url | http://psasir.upm.edu.my/id/eprint/57159/1/Composite%20group%20of%20explicit%20Runge-Kutta%20methods.pdf |
| work_keys_str_mv | AT abdhamidfatinnadiah compositegroupofexplicitrungekuttamethods AT rabieifaranak compositegroupofexplicitrungekuttamethods AT ismailfudziah compositegroupofexplicitrungekuttamethods |