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Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five

In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power serie...

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Main Authors: Omar, Zurni, Abdelrahim, Ra’ft
Format: Article
Language:English
Published: 2016
Subjects:
QA75 Electronic computers. Computer science
Online Access:http://repo.uum.edu.my/27961/1/IJPAM%20109%204%202016%20763%20777.pdf
http://repo.uum.edu.my/27961/
http://doi.org/10.12732/ijpam.v109i4.1
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spelling my.uum.repo.279612020-12-13T06:10:21Z http://repo.uum.edu.my/27961/ Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five Omar, Zurni Abdelrahim, Ra’ft QA75 Electronic computers. Computer science In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power series at $x_n $ and all off-step points and collocating its fourth derivative at all points in the selected interval. The method derived is proven to be consistent, zero stable and convergent with order five. Taylor’s series is used to supply the starting values for the implementation of the method while the performance of the method is tasted by solving linear and non-linear problems. 2016 Article PeerReviewed application/pdf en http://repo.uum.edu.my/27961/1/IJPAM%20109%204%202016%20763%20777.pdf Omar, Zurni and Abdelrahim, Ra’ft (2016) Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five. International Journal of Pure and Apllied Mathematics, 109 (4). pp. 763-777. ISSN 1311-8080 http://doi.org/10.12732/ijpam.v109i4.1 doi:10.12732/ijpam.v109i4.1
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Institutional Repository
url_provider http://repo.uum.edu.my/
language English
topic QA75 Electronic computers. Computer science
spellingShingle QA75 Electronic computers. Computer science
Omar, Zurni
Abdelrahim, Ra’ft
Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
description In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power series at $x_n $ and all off-step points and collocating its fourth derivative at all points in the selected interval. The method derived is proven to be consistent, zero stable and convergent with order five. Taylor’s series is used to supply the starting values for the implementation of the method while the performance of the method is tasted by solving linear and non-linear problems.
format Article
author Omar, Zurni
Abdelrahim, Ra’ft
author_facet Omar, Zurni
Abdelrahim, Ra’ft
author_sort Omar, Zurni
title Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
title_short Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
title_full Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
title_fullStr Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
title_full_unstemmed Direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
title_sort direct solution of fourth order ordinary differential equations using a one step hybrid block method of order five
publishDate 2016
url http://repo.uum.edu.my/27961/1/IJPAM%20109%204%202016%20763%20777.pdf
http://repo.uum.edu.my/27961/
http://doi.org/10.12732/ijpam.v109i4.1
_version_ 1687396251237089280
score 13.211869

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