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 Runge-Kutta method. Therefore the new scheme is computationally mor...

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Main Authors:	Faranak Rabiei, Fudziah Ismail, Mohamed Suleiman
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2013
Online Access:	http://journalarticle.ukm.my/6635/ http://journalarticle.ukm.my/6635/ http://journalarticle.ukm.my/6635/1/20_Faranak_Rabiei.pdf

id	ukm-6635
recordtype	eprints
spelling	ukm-66352016-12-14T06:41:45Z http://journalarticle.ukm.my/6635/ Improved Runge-Kutta methods for solving ordinary differential equations Faranak Rabiei, Fudziah Ismail, Mohamed Suleiman, 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 Runge-Kutta 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. Universiti Kebangsaan Malaysia 2013-11 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/6635/1/20_Faranak_Rabiei.pdf Faranak Rabiei, and Fudziah Ismail, and Mohamed Suleiman, (2013) Improved Runge-Kutta methods for solving ordinary differential equations. Sains Malaysiana, 42 (11). pp. 1679-1687. ISSN 0126-6039 http://www.ukm.my/jsm/
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
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 Runge-Kutta 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	Faranak Rabiei, Fudziah Ismail, Mohamed Suleiman,
spellingShingle	Faranak Rabiei, Fudziah Ismail, Mohamed Suleiman, Improved Runge-Kutta methods for solving ordinary differential equations
author_facet	Faranak Rabiei, Fudziah Ismail, Mohamed Suleiman,
author_sort	Faranak Rabiei,
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	Universiti Kebangsaan Malaysia
publishDate	2013
url	http://journalarticle.ukm.my/6635/ http://journalarticle.ukm.my/6635/ http://journalarticle.ukm.my/6635/1/20_Faranak_Rabiei.pdf
first_indexed	2023-09-18T19:47:28Z
last_indexed	2023-09-18T19:47:28Z
_version_	1777405996775243776

Improved Runge-Kutta methods for solving ordinary differential equations

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