Cover Image

Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')

The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u(4)=f(x,u,u′,u′′) and denoted as RKTF method. We presented the associated B-series and quad-colored tree t...

Full description

Saved in:
Bibliographic Details
Main Authors: Ghawadri, Nizam Ghannam Fayez, Senu, Norazak, Alshareeda, Firas Adel Fawzi, Ismail, Fudziah, Ibrahim, Zarina Bibi
Format: Article
Language:English
Published: MDPI 2019
Online Access:http://psasir.upm.edu.my/id/eprint/77861/1/77861.pdf
http://psasir.upm.edu.my/id/eprint/77861/
https://www.mdpi.com/2073-8994/11/2/246
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.77861
record_format eprints
spelling my.upm.eprints.778612020-05-04T17:37:48Z http://psasir.upm.edu.my/id/eprint/77861/ Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'') Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u(4)=f(x,u,u′,u′′) and denoted as RKTF method. We presented the associated B-series and quad-colored tree theory with the aim of deriving the prerequisites of the said order. Depending on the order conditions, the method with algebraic order four with a three-stage and order five with a four-stage denoted as RKTF4 and RKTF5 are discussed, respectively. Numerical outcomes are offered to interpret the accuracy and efficacy of the new techniques via comparisons with various currently available RK techniques after converting the problems into a system of first-order ODE systems. Application of the new methods in real-life problems in ship dynamics is discussed. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/77861/1/77861.pdf Ghawadri, Nizam Ghannam Fayez and Senu, Norazak and Alshareeda, Firas Adel Fawzi and Ismail, Fudziah and Ibrahim, Zarina Bibi (2019) Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u''). Symmetry, 11 (2). art. no. 246. pp. 1-30. ISSN 2073-8994 https://www.mdpi.com/2073-8994/11/2/246 10.3390/sym11020246
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 The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u(4)=f(x,u,u′,u′′) and denoted as RKTF method. We presented the associated B-series and quad-colored tree theory with the aim of deriving the prerequisites of the said order. Depending on the order conditions, the method with algebraic order four with a three-stage and order five with a four-stage denoted as RKTF4 and RKTF5 are discussed, respectively. Numerical outcomes are offered to interpret the accuracy and efficacy of the new techniques via comparisons with various currently available RK techniques after converting the problems into a system of first-order ODE systems. Application of the new methods in real-life problems in ship dynamics is discussed.
format Article
author Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Alshareeda, Firas Adel Fawzi
Ismail, Fudziah
Ibrahim, Zarina Bibi
spellingShingle Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Alshareeda, Firas Adel Fawzi
Ismail, Fudziah
Ibrahim, Zarina Bibi
Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
author_facet Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Alshareeda, Firas Adel Fawzi
Ismail, Fudziah
Ibrahim, Zarina Bibi
author_sort Ghawadri, Nizam Ghannam Fayez
title Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
title_short Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
title_full Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
title_fullStr Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
title_full_unstemmed Explicit integrator of Runge-Kutta type for direct solution of u(4) = f(x, u, u', u'')
title_sort explicit integrator of runge-kutta type for direct solution of u(4) = f(x, u, u', u'')
publisher MDPI
publishDate 2019
url http://psasir.upm.edu.my/id/eprint/77861/1/77861.pdf
http://psasir.upm.edu.my/id/eprint/77861/
https://www.mdpi.com/2073-8994/11/2/246
_version_ 1665896045418119168
score 13.211869

Similar Items