Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)

This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs...

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Main Authors:	Nur Zahidah Mukhtar, Zanariah Abdul Majid, Fudziah Ismail, Mohamed Suleiman
Format:	Article
Published:	Penerbit Universiti Kebangsaan Malaysia 2011
Online Access:	http://journalarticle.ukm.my/3456/ http://journalarticle.ukm.my/3456/

id	ukm-3456
recordtype	eprints
spelling	ukm-34562012-02-19T05:06:35Z http://journalarticle.ukm.my/3456/ Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta) Nur Zahidah Mukhtar, Zanariah Abdul Majid, Fudziah Ismail , Mohamed Suleiman, This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at three points simultaneously by integrating the coefficients over the closest point in the block. The stability region of the block method is also studied. The numerical results obtained shows that the proposed method is more efficient compared to existing block methods in terms of total steps and execution time. Penerbit Universiti Kebangsaan Malaysia 2011 Article PeerReviewed Nur Zahidah Mukhtar, and Zanariah Abdul Majid, and Fudziah Ismail , and Mohamed Suleiman, (2011) Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta). Journal of Quality Measurement and Analysis, 7 (2). pp. 145-154. ISSN 1823-5670 http://www.ukm.my/ppsmfst/jqma/index2.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
description	This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at three points simultaneously by integrating the coefficients over the closest point in the block. The stability region of the block method is also studied. The numerical results obtained shows that the proposed method is more efficient compared to existing block methods in terms of total steps and execution time.
format	Article
author	Nur Zahidah Mukhtar, Zanariah Abdul Majid, Fudziah Ismail , Mohamed Suleiman,
spellingShingle	Nur Zahidah Mukhtar, Zanariah Abdul Majid, Fudziah Ismail , Mohamed Suleiman, Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
author_facet	Nur Zahidah Mukhtar, Zanariah Abdul Majid, Fudziah Ismail , Mohamed Suleiman,
author_sort	Nur Zahidah Mukhtar,
title	Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
title_short	Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
title_full	Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
title_fullStr	Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
title_full_unstemmed	Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)
title_sort	solutions of general second order odes using direct block method of runge-kutta type.(penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis runge-kutta)
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2011
url	http://journalarticle.ukm.my/3456/ http://journalarticle.ukm.my/3456/
first_indexed	2023-09-18T19:38:49Z
last_indexed	2023-09-18T19:38:49Z
_version_	1777405452125995008

Solutions of general second order ODEs using direct block method of runge-kutta type.(Penyelesaian bagi persamaan pembezaan biasa umum peringkat kedua dengan kaedah blok langsung jenis Runge-Kutta)

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