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Hybrid methods for direct integration of special third Order ordinary differential equations

In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs),y'''=f(x,y) ; namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of t...

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Main Authors: Jikantoro, Yusuf Dauda, Ismail, Fudziah, Senu, Norazak, Ibrahim, Zarina Bibi
Format: Article
Language:English
Published: Elsevier 2018
Online Access:http://psasir.upm.edu.my/id/eprint/74527/1/Hybrid%20methods%20for%20direct%20integration%20of%20special%20third%20Order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/74527/
https://www.sciencedirect.com/science/article/pii/S0096300317306926#!
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spelling my.upm.eprints.745272019-12-05T03:30:35Z http://psasir.upm.edu.my/id/eprint/74527/ Hybrid methods for direct integration of special third Order ordinary differential equations Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak Ibrahim, Zarina Bibi In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs),y'''=f(x,y) ; namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of the HMTD methods is investigated. The main result of the paper is a theorem that generates algebraic order conditions of the methods that are analogous to those of two-step hybrid method. A three-stage explicit HMTD is constructed. Results from numerical experiment suggest the superiority of the new method over several existing methods considered in the paper. Elsevier 2018-03 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/74527/1/Hybrid%20methods%20for%20direct%20integration%20of%20special%20third%20Order%20ordinary%20differential%20equations.pdf Jikantoro, Yusuf Dauda and Ismail, Fudziah and Senu, Norazak and Ibrahim, Zarina Bibi (2018) Hybrid methods for direct integration of special third Order ordinary differential equations. Applied Mathematics and Computation, 320. 452 - 463. ISSN 0096-3003 https://www.sciencedirect.com/science/article/pii/S0096300317306926#! 10.1016/j.amc.2017.10.003
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 In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs),y'''=f(x,y) ; namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of the HMTD methods is investigated. The main result of the paper is a theorem that generates algebraic order conditions of the methods that are analogous to those of two-step hybrid method. A three-stage explicit HMTD is constructed. Results from numerical experiment suggest the superiority of the new method over several existing methods considered in the paper.
format Article
author Jikantoro, Yusuf Dauda
Ismail, Fudziah
Senu, Norazak
Ibrahim, Zarina Bibi
spellingShingle Jikantoro, Yusuf Dauda
Ismail, Fudziah
Senu, Norazak
Ibrahim, Zarina Bibi
Hybrid methods for direct integration of special third Order ordinary differential equations
author_facet Jikantoro, Yusuf Dauda
Ismail, Fudziah
Senu, Norazak
Ibrahim, Zarina Bibi
author_sort Jikantoro, Yusuf Dauda
title Hybrid methods for direct integration of special third Order ordinary differential equations
title_short Hybrid methods for direct integration of special third Order ordinary differential equations
title_full Hybrid methods for direct integration of special third Order ordinary differential equations
title_fullStr Hybrid methods for direct integration of special third Order ordinary differential equations
title_full_unstemmed Hybrid methods for direct integration of special third Order ordinary differential equations
title_sort hybrid methods for direct integration of special third order ordinary differential equations
publisher Elsevier
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/74527/1/Hybrid%20methods%20for%20direct%20integration%20of%20special%20third%20Order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/74527/
https://www.sciencedirect.com/science/article/pii/S0096300317306926#!
_version_ 1654961589650980864
score 13.211869

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