Implementation of four-point fully implicit block method for solving ordinary differential equations
This paper describes the development of a four-point fully implicit block method for solving first order ordinary differential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at four points simultaneously. The method developed is su...
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| Format: | Article |
| Language: | English English |
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Elsevier
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7790/1/Implementation%20of%20four.pdf |
| _version_ | 1825944274555895808 |
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| author | Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | Abdul Majid, Zanariah |
| collection | UPM |
| description | This paper describes the development of a four-point fully implicit block method for solving first order ordinary differential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non-stiff and mildly stiff differential systems. The performances of the four-point block method are compared in terms of maximum error, total number of steps and execution times to the non-block method 1PVSO in [Z. Omar, Developing parallel block methods for solving higher order ODEs directly, Ph.D. Thesis, University Putra Malaysia, Malaysia, 1999].
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| first_indexed | 2024-03-06T07:13:16Z |
| format | Article |
| id | upm.eprints-7790 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:13:16Z |
| publishDate | 2007 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-77902015-12-08T04:34:15Z http://psasir.upm.edu.my/id/eprint/7790/ Implementation of four-point fully implicit block method for solving ordinary differential equations Abdul Majid, Zanariah Suleiman, Mohamed This paper describes the development of a four-point fully implicit block method for solving first order ordinary differential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non-stiff and mildly stiff differential systems. The performances of the four-point block method are compared in terms of maximum error, total number of steps and execution times to the non-block method 1PVSO in [Z. Omar, Developing parallel block methods for solving higher order ODEs directly, Ph.D. Thesis, University Putra Malaysia, Malaysia, 1999]. Elsevier 2007 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7790/1/Implementation%20of%20four.pdf Abdul Majid, Zanariah and Suleiman, Mohamed (2007) Implementation of four-point fully implicit block method for solving ordinary differential equations. Applied Mathematics and Computation, 184 (2). pp. 514-522. ISSN 0096-3003 http://dx.doi.org/10.1016/j.amc.2006.05.169 10.1016/j.amc.2006.05.169 English |
| spellingShingle | Abdul Majid, Zanariah Suleiman, Mohamed Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title | Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title_full | Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title_fullStr | Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title_full_unstemmed | Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title_short | Implementation of four-point fully implicit block method for solving ordinary differential equations |
| title_sort | implementation of four point fully implicit block method for solving ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/7790/1/Implementation%20of%20four.pdf |
| work_keys_str_mv | AT abdulmajidzanariah implementationoffourpointfullyimplicitblockmethodforsolvingordinarydifferentialequations AT suleimanmohamed implementationoffourpointfullyimplicitblockmethodforsolvingordinarydifferentialequations |