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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| Format: | Article |
| Language: | English |
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Elsevier
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/74527/ http://psasir.upm.edu.my/id/eprint/74527/1/Hybrid%20methods%20for%20direct%20integration%20of%20special%20third%20Order%20ordinary%20differential%20equations.pdf |
| _version_ | 1848857513671262208 |
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| author | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak Ibrahim, Zarina Bibi |
| author_facet | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak Ibrahim, Zarina Bibi |
| author_sort | Jikantoro, Yusuf Dauda |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T11:58:45Z |
| format | Article |
| id | upm-74527 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:58:45Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Jikantoro, Yusuf Dauda Ismail, Fudziah Senu, Norazak Ibrahim, Zarina Bibi Hybrid methods for direct integration of special third Order ordinary differential equations |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/74527/ http://psasir.upm.edu.my/id/eprint/74527/ http://psasir.upm.edu.my/id/eprint/74527/ http://psasir.upm.edu.my/id/eprint/74527/1/Hybrid%20methods%20for%20direct%20integration%20of%20special%20third%20Order%20ordinary%20differential%20equations.pdf |