Block multistep methods based on rational approximants
In this study, the concept of block multistep methods based on rational approximants is introduced for the numerical solution of first order initial value problems. These numerical methods are also called rational block multistep methods.The main reason to consider block multistep methods in rationa...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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2014
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/12694/1/Bl.pdf |
| _version_ | 1825803049755475968 |
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| author | Teh, Yuan Ying Omar, Zurni Mansor, Kamarun Hizam |
| author_facet | Teh, Yuan Ying Omar, Zurni Mansor, Kamarun Hizam |
| author_sort | Teh, Yuan Ying |
| collection | UUM |
| description | In this study, the concept of block multistep methods based on rational approximants is introduced for the numerical solution of first order initial value problems. These numerical methods are also called rational block multistep methods.The main reason to consider block multistep methods in rational setting, is to improve the numerical accuracy and absolute stability property of existing block multistep methods that are based on polynomial approximants.For this pilot study, a 2-point explicit rational block multistep method is developed.Local truncation error and stability analysis for this new method are included as well.Numerical experimentations and results using some test problems are presented.Numerical results are satisfying in terms of numerical accuracy. Finally, future issues on the developments of rational block multistep methods are discussed. |
| first_indexed | 2024-07-04T05:50:33Z |
| format | Conference or Workshop Item |
| id | uum-12694 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:50:33Z |
| publishDate | 2014 |
| record_format | eprints |
| spelling | uum-126942016-05-26T01:41:20Z https://repo.uum.edu.my/id/eprint/12694/ Block multistep methods based on rational approximants Teh, Yuan Ying Omar, Zurni Mansor, Kamarun Hizam QA Mathematics In this study, the concept of block multistep methods based on rational approximants is introduced for the numerical solution of first order initial value problems. These numerical methods are also called rational block multistep methods.The main reason to consider block multistep methods in rational setting, is to improve the numerical accuracy and absolute stability property of existing block multistep methods that are based on polynomial approximants.For this pilot study, a 2-point explicit rational block multistep method is developed.Local truncation error and stability analysis for this new method are included as well.Numerical experimentations and results using some test problems are presented.Numerical results are satisfying in terms of numerical accuracy. Finally, future issues on the developments of rational block multistep methods are discussed. 2014-12-17 Conference or Workshop Item PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/12694/1/Bl.pdf Teh, Yuan Ying and Omar, Zurni and Mansor, Kamarun Hizam (2014) Block multistep methods based on rational approximants. In: 3rd International Conference on Mathematical Sciences, 17–19 December 2013, Kuala Lumpur, Malaysia. http://dx.doi.org/10.1063/1.4882460 doi:10.1063/1.4882460 doi:10.1063/1.4882460 |
| spellingShingle | QA Mathematics Teh, Yuan Ying Omar, Zurni Mansor, Kamarun Hizam Block multistep methods based on rational approximants |
| title | Block multistep methods based on rational approximants |
| title_full | Block multistep methods based on rational approximants |
| title_fullStr | Block multistep methods based on rational approximants |
| title_full_unstemmed | Block multistep methods based on rational approximants |
| title_short | Block multistep methods based on rational approximants |
| title_sort | block multistep methods based on rational approximants |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/12694/1/Bl.pdf |
| work_keys_str_mv | AT tehyuanying blockmultistepmethodsbasedonrationalapproximants AT omarzurni blockmultistepmethodsbasedonrationalapproximants AT mansorkamarunhizam blockmultistepmethodsbasedonrationalapproximants |