Variable step direct block multistep method for general second order ODEs
Direct block multistep method is developed for the numerical solution of second order ordinary differential equations (ODEs). This method was designed for computing the solution at four points simultaneously using variable step size. The development of this method based on numerical integration and...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing LLC
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57568/1/Variable%20step%20direct%20block%20multistep%20method%20for%20general%20second%20order%20ODEs.pdf |
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| author | Waeleh, Nazreen Abdul Majid, Zanariah |
| author_facet | Waeleh, Nazreen Abdul Majid, Zanariah |
| author_sort | Waeleh, Nazreen |
| collection | UPM |
| description | Direct block multistep method is developed for the numerical solution of second order ordinary differential equations (ODEs). This method was designed for computing the solution at four points simultaneously using variable step size. The development of this method based on numerical integration and using interpolation approach which are similar to the Adams method. In order to gain an efficient and reliable numerical approximation, this developed block method is implemented in the predictor corrector mode using simple iteration technique. This method has also been proven as a convergence method under suitable conditions of stability and consistency. Several tested problems are taken into account in the numerical experiments and were compared with the existing method. The results obtained showed that this developed block method managed to produce good results. |
| first_indexed | 2024-03-06T09:29:47Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57568 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:47Z |
| publishDate | 2014 |
| publisher | AIP Publishing LLC |
| record_format | dspace |
| spelling | upm.eprints-575682017-10-24T05:16:26Z http://psasir.upm.edu.my/id/eprint/57568/ Variable step direct block multistep method for general second order ODEs Waeleh, Nazreen Abdul Majid, Zanariah Direct block multistep method is developed for the numerical solution of second order ordinary differential equations (ODEs). This method was designed for computing the solution at four points simultaneously using variable step size. The development of this method based on numerical integration and using interpolation approach which are similar to the Adams method. In order to gain an efficient and reliable numerical approximation, this developed block method is implemented in the predictor corrector mode using simple iteration technique. This method has also been proven as a convergence method under suitable conditions of stability and consistency. Several tested problems are taken into account in the numerical experiments and were compared with the existing method. The results obtained showed that this developed block method managed to produce good results. AIP Publishing LLC 2014 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57568/1/Variable%20step%20direct%20block%20multistep%20method%20for%20general%20second%20order%20ODEs.pdf Waeleh, Nazreen and Abdul Majid, Zanariah (2014) Variable step direct block multistep method for general second order ODEs. In: 3rd International Conference on Fundamental and Applied Sciences (ICFAS 2014), 3-5 June 2014, Kuala Lumpur Convention Centre, Kuala Lumpur. (pp. 176-183). 10.1063/1.4898463 |
| spellingShingle | Waeleh, Nazreen Abdul Majid, Zanariah Variable step direct block multistep method for general second order ODEs |
| title | Variable step direct block multistep method for general second order ODEs |
| title_full | Variable step direct block multistep method for general second order ODEs |
| title_fullStr | Variable step direct block multistep method for general second order ODEs |
| title_full_unstemmed | Variable step direct block multistep method for general second order ODEs |
| title_short | Variable step direct block multistep method for general second order ODEs |
| title_sort | variable step direct block multistep method for general second order odes |
| url | http://psasir.upm.edu.my/id/eprint/57568/1/Variable%20step%20direct%20block%20multistep%20method%20for%20general%20second%20order%20ODEs.pdf |
| work_keys_str_mv | AT waelehnazreen variablestepdirectblockmultistepmethodforgeneralsecondorderodes AT abdulmajidzanariah variablestepdirectblockmultistepmethodforgeneralsecondorderodes |