Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations
In this paper, fourth-order improved Runge–Kutta method (IRKD) for directly solving a special third-order ordinary differential equation is constructed. The fourth-order IRKD method has a lower number of function evaluations compared with the fourth-order Runge–Kutta method. The stability polynomial...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57202/1/Fourth-order%20improved%20Runge%E2%80%93Kutta%20method%20for%20directly%20solving%20special%20third-order%20ordinary%20differential%20equations.pdf |
| _version_ | 1825931565895516160 |
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| author | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak |
| author_facet | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak |
| author_sort | Hussain, Kasim Abbas |
| collection | UPM |
| description | In this paper, fourth-order improved Runge–Kutta method (IRKD) for directly solving a special third-order ordinary differential equation is constructed. The fourth-order IRKD method has a lower number of function evaluations compared with the fourth-order Runge–Kutta method. The stability polynomial of the method is given. Numerical comparisons are also performed using the existing Runge–Kutta method after reducing the problems into a system of first-order equations and solving them, and direct RKD method for solving special third-order ordinary differential equations. Numerical examples are presented to illustrate the efficiency and the accuracy of the new method in terms of number of function evaluations as well as max absolute error. |
| first_indexed | 2024-03-06T09:28:40Z |
| format | Article |
| id | upm.eprints-57202 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:40Z |
| publishDate | 2017 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-572022017-09-08T10:29:43Z http://psasir.upm.edu.my/id/eprint/57202/ Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak In this paper, fourth-order improved Runge–Kutta method (IRKD) for directly solving a special third-order ordinary differential equation is constructed. The fourth-order IRKD method has a lower number of function evaluations compared with the fourth-order Runge–Kutta method. The stability polynomial of the method is given. Numerical comparisons are also performed using the existing Runge–Kutta method after reducing the problems into a system of first-order equations and solving them, and direct RKD method for solving special third-order ordinary differential equations. Numerical examples are presented to illustrate the efficiency and the accuracy of the new method in terms of number of function evaluations as well as max absolute error. Springer 2017 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57202/1/Fourth-order%20improved%20Runge%E2%80%93Kutta%20method%20for%20directly%20solving%20special%20third-order%20ordinary%20differential%20equations.pdf Hussain, Kasim Abbas and Ismail, Fudziah and Senu, Norazak and Rabiei, Faranak (2017) Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations. Iranian Journal of Science and Technology, Transactions A: Science, 41 (2). pp. 429-437. ISSN 1028-6276; ESSN: 2364-1819 https://rd.springer.com/article/10.1007/s40995-017-0258-1 10.1007/s40995-017-0258-1 |
| spellingShingle | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title | Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title_full | Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title_fullStr | Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title_full_unstemmed | Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title_short | Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations |
| title_sort | fourth order improved runge kutta method for directly solving special third order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/57202/1/Fourth-order%20improved%20Runge%E2%80%93Kutta%20method%20for%20directly%20solving%20special%20third-order%20ordinary%20differential%20equations.pdf |
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