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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://www.ukm.my/ppsmfst/jqma/index2.html
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spelling my-ukm.journal.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
institution Universiti Kebangsaan Malaysia
building Perpustakaan Tun Sri Lanang Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Kebangsaan Malaysia
content_source UKM Journal Article Repository
url_provider http://journalarticle.ukm.my/
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://www.ukm.my/ppsmfst/jqma/index2.html
_version_ 1643735728912334848
score 13.211869

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