Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly.
This paper focused mainly on deriving explicit and implicit 3-point block methods of constant step size using linear difference operator for solving special second order ordinary differential equations (ODEs). The methods compute the solutions of the ODEs at three points simultaneously. Regions of...
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| Format: | Article |
| Language: | English English |
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Hikari Ltd
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/14652/ http://psasir.upm.edu.my/id/eprint/14652/1/Explicit%20and%20implicit%203.pdf |
| _version_ | 1848842453431353344 |
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| author | Ismail, Fudziah Yap, Lee Ken Othman, Mohamed |
| author_facet | Ismail, Fudziah Yap, Lee Ken Othman, Mohamed |
| author_sort | Ismail, Fudziah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper focused mainly on deriving explicit and implicit 3-point block methods of constant step size using linear difference operator for solving special second order ordinary differential equations (ODEs). The methods compute the solutions of the ODEs at three points simultaneously. Regions of stability for both the explicit and implicit block methods are presented. A standard set of problems are solved using the new methods and the numerical results are compared when the same set of problems are solved using existing methods. The results suggest a significant improvement in efficiency of the new methods in terms of number of steps and accuracy. |
| first_indexed | 2025-11-15T07:59:22Z |
| format | Article |
| id | upm-14652 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:59:22Z |
| publishDate | 2009 |
| publisher | Hikari Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-146522015-09-29T07:48:09Z http://psasir.upm.edu.my/id/eprint/14652/ Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. Ismail, Fudziah Yap, Lee Ken Othman, Mohamed This paper focused mainly on deriving explicit and implicit 3-point block methods of constant step size using linear difference operator for solving special second order ordinary differential equations (ODEs). The methods compute the solutions of the ODEs at three points simultaneously. Regions of stability for both the explicit and implicit block methods are presented. A standard set of problems are solved using the new methods and the numerical results are compared when the same set of problems are solved using existing methods. The results suggest a significant improvement in efficiency of the new methods in terms of number of steps and accuracy. Hikari Ltd 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/14652/1/Explicit%20and%20implicit%203.pdf Ismail, Fudziah and Yap, Lee Ken and Othman, Mohamed (2009) Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. International Journal of Mathematical Analysis, 3 (5). pp. 239-254. ISSN 1312-8876; ESSN: 1314-7579 http://www.m-hikari.com/ijma/index.html English |
| spellingShingle | Ismail, Fudziah Yap, Lee Ken Othman, Mohamed Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title | Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title_full | Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title_fullStr | Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title_full_unstemmed | Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title_short | Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| title_sort | explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. |
| url | http://psasir.upm.edu.my/id/eprint/14652/ http://psasir.upm.edu.my/id/eprint/14652/ http://psasir.upm.edu.my/id/eprint/14652/1/Explicit%20and%20implicit%203.pdf |