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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/77861/1/77861.pdf |
| _version_ | 1796980370221039616 |
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| author | Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_facet | Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_sort | Ghawadri, Nizam Ghannam Fayez |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T10:22:01Z |
| format | Article |
| id | upm.eprints-77861 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:22:01Z |
| publishDate | 2019 |
| publisher | MDPI |
| record_format | dspace |
| spelling | 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 |
| 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'') |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/77861/1/77861.pdf |
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