Solving general fourth order ODEs directly using four point block method
A four point block method based on Adams type formulae is proposed for solving general fourth order ordinary differential equations (ODEs) directly. This four point block method will be implemented in predictor corrector mode and the corrector will be iterated to convergent. The numerical solution...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17953/ http://psasir.upm.edu.my/id/eprint/17953/1/ID%2017953.pdf |
| _version_ | 1848843385372147712 |
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| author | Abdul Majid, Zanariah Waeleh, Nazreen Ismail, Fudziah Suleiman, Mohamed |
| author_facet | Abdul Majid, Zanariah Waeleh, Nazreen Ismail, Fudziah Suleiman, Mohamed |
| author_sort | Abdul Majid, Zanariah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A four point block method based on Adams type formulae is proposed for solving general fourth order ordinary differential equations (ODEs) directly. This four point block method will be implemented in predictor corrector mode and the corrector will be iterated to convergent. The numerical solution will be computed at four equally steps simultaneously. Most of the existence researches involving higher order ODEs will reduced the problem to a system of first order ODEs and this approach is obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the fourth order ODEs directly without reducing it to first order equations. Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using variable step size in order to determine the approximated solutions. Numerical results shown that the four point block method were superior compared to the existing method. It is clearly proved that the four point block is able to produce acceptable results for solving fourth order ODEs. |
| first_indexed | 2025-11-15T08:14:11Z |
| format | Conference or Workshop Item |
| id | upm-17953 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:14:11Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-179532017-09-28T02:56:42Z http://psasir.upm.edu.my/id/eprint/17953/ Solving general fourth order ODEs directly using four point block method Abdul Majid, Zanariah Waeleh, Nazreen Ismail, Fudziah Suleiman, Mohamed A four point block method based on Adams type formulae is proposed for solving general fourth order ordinary differential equations (ODEs) directly. This four point block method will be implemented in predictor corrector mode and the corrector will be iterated to convergent. The numerical solution will be computed at four equally steps simultaneously. Most of the existence researches involving higher order ODEs will reduced the problem to a system of first order ODEs and this approach is obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the fourth order ODEs directly without reducing it to first order equations. Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using variable step size in order to determine the approximated solutions. Numerical results shown that the four point block method were superior compared to the existing method. It is clearly proved that the four point block is able to produce acceptable results for solving fourth order ODEs. 2011 Conference or Workshop Item NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17953/1/ID%2017953.pdf Abdul Majid, Zanariah and Waeleh, Nazreen and Ismail, Fudziah and Suleiman, Mohamed (2011) Solving general fourth order ODEs directly using four point block method. In: International Conference on Applied Analysis and Algebra (ICAAA2011), 29 June-2 July 2011, Istanbul, Turkey. . |
| spellingShingle | Abdul Majid, Zanariah Waeleh, Nazreen Ismail, Fudziah Suleiman, Mohamed Solving general fourth order ODEs directly using four point block method |
| title | Solving general fourth order ODEs directly using four point block method |
| title_full | Solving general fourth order ODEs directly using four point block method |
| title_fullStr | Solving general fourth order ODEs directly using four point block method |
| title_full_unstemmed | Solving general fourth order ODEs directly using four point block method |
| title_short | Solving general fourth order ODEs directly using four point block method |
| title_sort | solving general fourth order odes directly using four point block method |
| url | http://psasir.upm.edu.my/id/eprint/17953/ http://psasir.upm.edu.my/id/eprint/17953/1/ID%2017953.pdf |