Numerical solution of differential algebraic equations (DAEs) by mix-multistep method
Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2013
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/57328/ http://psasir.upm.edu.my/id/eprint/57328/1/Numerical%20solution%20of%20differential%20algebraic%20equations%20%28DAEs%29%20by%20mix-multistep%20method.pdf |
| _version_ | 1848853334389161984 |
|---|---|
| author | Rahim, Yong Faezah Suleiman, Mohamed Ibrahim, Zarina Bibi |
| author_facet | Rahim, Yong Faezah Suleiman, Mohamed Ibrahim, Zarina Bibi |
| author_sort | Rahim, Yong Faezah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However, not all of the ODEs in DAE system are stiff. In this paper, we describe a new technique for solving DAE, where the ODEs are treated as non-stiff at the start of the integration and putting the non-stiff ODEs into stiff subsystem should instability occurs. Adams type of method is used to solve the non-stiff part and BDF method for solving the stiff part. This strategy is shown to be competitive in terms of computational effort and accuracy. Numerical experiments are presented to validate its efficiency. |
| first_indexed | 2025-11-15T10:52:19Z |
| format | Conference or Workshop Item |
| id | upm-57328 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:19Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-573282017-09-26T04:04:31Z http://psasir.upm.edu.my/id/eprint/57328/ Numerical solution of differential algebraic equations (DAEs) by mix-multistep method Rahim, Yong Faezah Suleiman, Mohamed Ibrahim, Zarina Bibi Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However, not all of the ODEs in DAE system are stiff. In this paper, we describe a new technique for solving DAE, where the ODEs are treated as non-stiff at the start of the integration and putting the non-stiff ODEs into stiff subsystem should instability occurs. Adams type of method is used to solve the non-stiff part and BDF method for solving the stiff part. This strategy is shown to be competitive in terms of computational effort and accuracy. Numerical experiments are presented to validate its efficiency. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57328/1/Numerical%20solution%20of%20differential%20algebraic%20equations%20%28DAEs%29%20by%20mix-multistep%20method.pdf Rahim, Yong Faezah and Suleiman, Mohamed and Ibrahim, Zarina Bibi (2013) Numerical solution of differential algebraic equations (DAEs) by mix-multistep method. In: 3rd International Conference on Mathematical Sciences (ICMS3), 17-19 Dec. 2013, Kuala Lumpur, Malaysia. (pp. 170-178). 10.1063/1.4882484 |
| spellingShingle | Rahim, Yong Faezah Suleiman, Mohamed Ibrahim, Zarina Bibi Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title | Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title_full | Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title_fullStr | Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title_full_unstemmed | Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title_short | Numerical solution of differential algebraic equations (DAEs) by mix-multistep method |
| title_sort | numerical solution of differential algebraic equations (daes) by mix-multistep method |
| url | http://psasir.upm.edu.my/id/eprint/57328/ http://psasir.upm.edu.my/id/eprint/57328/ http://psasir.upm.edu.my/id/eprint/57328/1/Numerical%20solution%20of%20differential%20algebraic%20equations%20%28DAEs%29%20by%20mix-multistep%20method.pdf |