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Extra derivative implicit block methods for integrating general second order initial value problems

This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one poin...

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Main Authors: Turki, Mohammed Yousif, Ismail, Fudziah, Senu, Norazak
Format: Article
Language:English
Published: Universiti Putra Malaysia Press 2020
Online Access:http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf
http://psasir.upm.edu.my/id/eprint/80784/
http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-1902-2020
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spelling my.upm.eprints.807842021-08-18T01:24:46Z http://psasir.upm.edu.my/id/eprint/80784/ Extra derivative implicit block methods for integrating general second order initial value problems Turki, Mohammed Yousif Ismail, Fudziah Senu, Norazak This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one point at a time directly without reducing the equation into the first order system of ordinary differential equations. In the derivation of the method, the higher derivative of the problem is incorporated into the formula to enhance the efficiency of the proposed methods. The order and zero- stability of the methods are also presented. Numerical results presented show the efficiency of these methods compared to the existing block methods. Universiti Putra Malaysia Press 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf Turki, Mohammed Yousif and Ismail, Fudziah and Senu, Norazak (2020) Extra derivative implicit block methods for integrating general second order initial value problems. Pertanika Journal of Science and Technology, 28 (3). pp. 951-966. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-1902-2020
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 This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one point at a time directly without reducing the equation into the first order system of ordinary differential equations. In the derivation of the method, the higher derivative of the problem is incorporated into the formula to enhance the efficiency of the proposed methods. The order and zero- stability of the methods are also presented. Numerical results presented show the efficiency of these methods compared to the existing block methods.
format Article
author Turki, Mohammed Yousif
Ismail, Fudziah
Senu, Norazak
spellingShingle Turki, Mohammed Yousif
Ismail, Fudziah
Senu, Norazak
Extra derivative implicit block methods for integrating general second order initial value problems
author_facet Turki, Mohammed Yousif
Ismail, Fudziah
Senu, Norazak
author_sort Turki, Mohammed Yousif
title Extra derivative implicit block methods for integrating general second order initial value problems
title_short Extra derivative implicit block methods for integrating general second order initial value problems
title_full Extra derivative implicit block methods for integrating general second order initial value problems
title_fullStr Extra derivative implicit block methods for integrating general second order initial value problems
title_full_unstemmed Extra derivative implicit block methods for integrating general second order initial value problems
title_sort extra derivative implicit block methods for integrating general second order initial value problems
publisher Universiti Putra Malaysia Press
publishDate 2020
url http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf
http://psasir.upm.edu.my/id/eprint/80784/
http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-1902-2020
_version_ 1709668986185056256
score 13.211869

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