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Improved Runge-Kutta methods for solving ordinary differential equations

In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more...

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Main Authors: Rabiei, Faranak, Ismail, Fudziah, Suleiman, Mohamed
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30892/1/Improved%20Runge.pdf
http://psasir.upm.edu.my/id/eprint/30892/
http://www.ukm.my/jsm/english_journals/vol42num11_2013/contentsVol42num11_2013.html
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spelling my.upm.eprints.308922016-02-02T02:36:30Z http://psasir.upm.edu.my/id/eprint/30892/ Improved Runge-Kutta methods for solving ordinary differential equations Rabiei, Faranak Ismail, Fudziah Suleiman, Mohamed In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods are obtained up to order five using Taylor series expansion and the third and fourth order methods with different stages are derived based on the order conditions. The free parameters are obtained through minimization of the error norm. Convergence of the method is proven and the stability regions are presented. To illustrate the efficiency of the method a number of problems are solved and numerical results showed that the method is more efficient compared with the existing Runge-Kutta method. Penerbit Universiti Kebangsaan Malaysia 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30892/1/Improved%20Runge.pdf Rabiei, Faranak and Ismail, Fudziah and Suleiman, Mohamed (2013) Improved Runge-Kutta methods for solving ordinary differential equations. Sains Malaysiana, 42 (11). pp. 1679-1687. ISSN 0026-6039 http://www.ukm.my/jsm/english_journals/vol42num11_2013/contentsVol42num11_2013.html
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods are obtained up to order five using Taylor series expansion and the third and fourth order methods with different stages are derived based on the order conditions. The free parameters are obtained through minimization of the error norm. Convergence of the method is proven and the stability regions are presented. To illustrate the efficiency of the method a number of problems are solved and numerical results showed that the method is more efficient compared with the existing Runge-Kutta method.
format Article
author Rabiei, Faranak
Ismail, Fudziah
Suleiman, Mohamed
spellingShingle Rabiei, Faranak
Ismail, Fudziah
Suleiman, Mohamed
Improved Runge-Kutta methods for solving ordinary differential equations
author_facet Rabiei, Faranak
Ismail, Fudziah
Suleiman, Mohamed
author_sort Rabiei, Faranak
title Improved Runge-Kutta methods for solving ordinary differential equations
title_short Improved Runge-Kutta methods for solving ordinary differential equations
title_full Improved Runge-Kutta methods for solving ordinary differential equations
title_fullStr Improved Runge-Kutta methods for solving ordinary differential equations
title_full_unstemmed Improved Runge-Kutta methods for solving ordinary differential equations
title_sort improved runge-kutta methods for solving ordinary differential equations
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30892/1/Improved%20Runge.pdf
http://psasir.upm.edu.my/id/eprint/30892/
http://www.ukm.my/jsm/english_journals/vol42num11_2013/contentsVol42num11_2013.html
_version_ 1643830197074526208
score 13.211869

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