A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly
The existing hybrid methods for solving ordinary differential equations were only derived using specific off-step points. Thus, this paper proposes a new four-step block method with three generalized off-step points for solving initial value problems of fourth order ordinary differential equations d...
Saved in:
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
2017
|
Subjects: | |
Online Access: | http://repo.uum.edu.my/27951/1/JKSU%20s%2029%204%202017%20401%20412.pdf http://repo.uum.edu.my/27951/ http://doi.org/10.1016/j.jksus.2017.06.003 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
my.uum.repo.27951 |
---|---|
record_format |
eprints |
spelling |
my.uum.repo.279512020-12-06T06:42:03Z http://repo.uum.edu.my/27951/ A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly Abdelrahim, Ra’ft Omar, Zurni QA75 Electronic computers. Computer science The existing hybrid methods for solving ordinary differential equations were only derived using specific off-step points. Thus, this paper proposes a new four-step block method with three generalized off-step points for solving initial value problems of fourth order ordinary differential equations directly. The strategy employed to develop this method is interpolating the basis function at ynþj; j ¼ 0ð1Þ3 and collocating the fourth derivative of the basis function at all points within the selected interval. The implementation of this method in a block-by-block fashion can overcome the setbacks of applying starting values and predictors which are created in predictor-corrector approach. The convergence analysis of the developed method is performed and the accuracy of the method is tested on several problems. The numerical results indicate that the new method outperforms the existing ones in terms of errors. In addition, the new method does not require much computation when compared with previous methods. 2017 Article PeerReviewed application/pdf en http://repo.uum.edu.my/27951/1/JKSU%20s%2029%204%202017%20401%20412.pdf Abdelrahim, Ra’ft and Omar, Zurni (2017) A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly. Journal of King Saud University - Science, 29. pp. 401-412. ISSN 10183647 http://doi.org/10.1016/j.jksus.2017.06.003 doi:10.1016/j.jksus.2017.06.003 |
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 Abdelrahim, Ra’ft Omar, Zurni A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
description |
The existing hybrid methods for solving ordinary differential equations were only derived using specific off-step points. Thus, this paper proposes a new four-step block method with three generalized off-step points for solving initial value problems of fourth order ordinary differential equations directly. The strategy employed to develop this method is interpolating the basis function at ynþj; j ¼ 0ð1Þ3 and collocating the fourth derivative of the basis function at all points within the selected interval. The implementation of this method in a block-by-block fashion can overcome the setbacks of applying starting values and predictors which are created in predictor-corrector approach. The convergence analysis of the developed method is performed and the accuracy of the method is tested on several problems. The numerical results
indicate that the new method outperforms the existing ones in terms of errors. In addition, the new method does not require much computation when compared with previous methods. |
format |
Article |
author |
Abdelrahim, Ra’ft Omar, Zurni |
author_facet |
Abdelrahim, Ra’ft Omar, Zurni |
author_sort |
Abdelrahim, Ra’ft |
title |
A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
title_short |
A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
title_full |
A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
title_fullStr |
A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
title_full_unstemmed |
A four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
title_sort |
four-step implicit block method with three generalized off-step points for solving fourth order initial value problems directly |
publishDate |
2017 |
url |
http://repo.uum.edu.my/27951/1/JKSU%20s%2029%204%202017%20401%20412.pdf http://repo.uum.edu.my/27951/ http://doi.org/10.1016/j.jksus.2017.06.003 |
_version_ |
1685581077024866304 |
score |
13.154949 |