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Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly

This paper proposes a new two-step hybrid block method with one generalized off-step point within each step to find the direct solution of second order ordinary differential equation. In deriving this method, a power series is adopted as an approximate solution and interpolated at points while its s...

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Main Authors: Mansor, Kamarun Hizam, Omar, Zurni, Rohni, AM
Format: Article
Published: JARDCS 2018
Subjects:
QA75 Electronic computers. Computer science
Online Access:http://repo.uum.edu.my/27942/
https://www.jardcs.org/backissues/abstract.php?archiveid=5938
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spelling my.uum.repo.279422020-12-02T07:13:59Z http://repo.uum.edu.my/27942/ Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly Mansor, Kamarun Hizam Omar, Zurni Rohni, AM QA75 Electronic computers. Computer science This paper proposes a new two-step hybrid block method with one generalized off-step point within each step to find the direct solution of second order ordinary differential equation. In deriving this method, a power series is adopted as an approximate solution and interpolated at points while its second derivatives collocated at all points in the given interval to obtain the main continuous scheme. This method generates the non-overlapping starting values using Taylor series. The analysis of the method such as order, zero stability, consistency and convergence is also discussed. The developed method was then compared with the existing methods in terms of accuracy and the results suggest that this method can be served as a viable alternative methods to solve directly initial value problems of second order ordinary differential equations. JARDCS 2018 Article PeerReviewed Mansor, Kamarun Hizam and Omar, Zurni and Rohni, AM (2018) Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly. Journal of Advanced Research in Dynamical and Control Systems, 13 (SI). pp. 1-17. ISSN 1943-023X https://www.jardcs.org/backissues/abstract.php?archiveid=5938
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/
topic QA75 Electronic computers. Computer science
spellingShingle QA75 Electronic computers. Computer science
Mansor, Kamarun Hizam
Omar, Zurni
Rohni, AM
Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
description This paper proposes a new two-step hybrid block method with one generalized off-step point within each step to find the direct solution of second order ordinary differential equation. In deriving this method, a power series is adopted as an approximate solution and interpolated at points while its second derivatives collocated at all points in the given interval to obtain the main continuous scheme. This method generates the non-overlapping starting values using Taylor series. The analysis of the method such as order, zero stability, consistency and convergence is also discussed. The developed method was then compared with the existing methods in terms of accuracy and the results suggest that this method can be served as a viable alternative methods to solve directly initial value problems of second order ordinary differential equations.
format Article
author Mansor, Kamarun Hizam
Omar, Zurni
Rohni, AM
author_facet Mansor, Kamarun Hizam
Omar, Zurni
Rohni, AM
author_sort Mansor, Kamarun Hizam
title Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
title_short Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
title_full Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
title_fullStr Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
title_full_unstemmed Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
title_sort generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly
publisher JARDCS
publishDate 2018
url http://repo.uum.edu.my/27942/
https://www.jardcs.org/backissues/abstract.php?archiveid=5938
_version_ 1685581075734069248
score 13.211869

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