Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divi...
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2006
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| Online Access: | http://psasir.upm.edu.my/id/eprint/18015/ http://psasir.upm.edu.my/id/eprint/18015/1/Direct%20integration%20implicit%20variable%20steps%20method%20for%20solving%20higher%20order%20systems%20of%20ordinary%20differential%20equations%20directly.pdf |
| _version_ | 1848843402402070528 |
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| author | Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | Abdul Majid, Zanariah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divided differences and integration coefficients in the code when using the variable step size or variable step size and order. The idea of developing this method is to store all the coefficients involved in the code. Thus, this strategy can avoid the lengthy computation of the coefficients during the implementation of the code as well as to improve the execution time. Numerical results are given to compare the efficiency of the developed method with the 1-point method of variable step size and order code (IPDVSO) in Omar (1999). |
| first_indexed | 2025-11-15T08:14:27Z |
| format | Article |
| id | upm-18015 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:14:27Z |
| publishDate | 2006 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-180152016-01-22T07:35:37Z http://psasir.upm.edu.my/id/eprint/18015/ Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly Abdul Majid, Zanariah Suleiman, Mohamed In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divided differences and integration coefficients in the code when using the variable step size or variable step size and order. The idea of developing this method is to store all the coefficients involved in the code. Thus, this strategy can avoid the lengthy computation of the coefficients during the implementation of the code as well as to improve the execution time. Numerical results are given to compare the efficiency of the developed method with the 1-point method of variable step size and order code (IPDVSO) in Omar (1999). Penerbit Universiti Kebangsaan Malaysia 2006-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/18015/1/Direct%20integration%20implicit%20variable%20steps%20method%20for%20solving%20higher%20order%20systems%20of%20ordinary%20differential%20equations%20directly.pdf Abdul Majid, Zanariah and Suleiman, Mohamed (2006) Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly. Sains Malaysiana, 35 (2). pp. 63-68. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol35num2_2006/vol35num2_06page63-68.html |
| spellingShingle | Abdul Majid, Zanariah Suleiman, Mohamed Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title | Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title_full | Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title_fullStr | Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title_full_unstemmed | Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title_short | Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| title_sort | direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly |
| url | http://psasir.upm.edu.my/id/eprint/18015/ http://psasir.upm.edu.my/id/eprint/18015/ http://psasir.upm.edu.my/id/eprint/18015/1/Direct%20integration%20implicit%20variable%20steps%20method%20for%20solving%20higher%20order%20systems%20of%20ordinary%20differential%20equations%20directly.pdf |