Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems
When finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative refinement or preconditioning, by carefully choos...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2910 |
| _version_ | 1797409055741837312 |
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| author | Richard Olatokunbo Akinola Ali Shokri Shao-Wen Yao Stephen Yakubu Kutchin |
| author_facet | Richard Olatokunbo Akinola Ali Shokri Shao-Wen Yao Stephen Yakubu Kutchin |
| author_sort | Richard Olatokunbo Akinola |
| collection | DOAJ |
| description | When finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative refinement or preconditioning, by carefully choosing the grid point used in deriving the discrete scheme from the continuous formulation. Results of numerical experiments show that the new scheme perform very well when compared with the exact solution and results from an earlier scheme. |
| first_indexed | 2024-03-09T04:08:46Z |
| format | Article |
| id | doaj.art-7ec26cf92d4a4009982acf0c36edd45f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:08:46Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7ec26cf92d4a4009982acf0c36edd45f2023-12-03T14:03:21ZengMDPI AGMathematics2227-73902022-08-011016291010.3390/math10162910Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value ProblemsRichard Olatokunbo Akinola0Ali Shokri1Shao-Wen Yao2Stephen Yakubu Kutchin3Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930105, NigeriaDepartment of Science, Faculty of Science, University of Maragheh, Maragheh 83111-55181, IranSchool of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, ChinaDepartment of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930105, NigeriaWhen finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative refinement or preconditioning, by carefully choosing the grid point used in deriving the discrete scheme from the continuous formulation. Results of numerical experiments show that the new scheme perform very well when compared with the exact solution and results from an earlier scheme.https://www.mdpi.com/2227-7390/10/16/2910ill-conditioninglinear multistep methodsorder(non)singularityunderdetermined |
| spellingShingle | Richard Olatokunbo Akinola Ali Shokri Shao-Wen Yao Stephen Yakubu Kutchin Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems Mathematics ill-conditioning linear multistep methods order (non)singularity underdetermined |
| title | Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems |
| title_full | Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems |
| title_fullStr | Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems |
| title_full_unstemmed | Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems |
| title_short | Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems |
| title_sort | circumventing ill conditioning arising from using linear multistep methods in approximating the solution of initial value problems |
| topic | ill-conditioning linear multistep methods order (non)singularity underdetermined |
| url | https://www.mdpi.com/2227-7390/10/16/2910 |
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