Adaptive integration algorithm for stiff ordinary differential equations
The accuracy of one adaptive integration algorithm is investigated. The accuracy of the discretization is estimated by comparing the discrete and exact stability factors. It is proved that the classical stiffness definition is sufficient for explicit schemes. The complexity of implicit schemes depe...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
1999-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/35670 |
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| _version_ | 1825197152626802688 |
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| author | Raimondas Čiegis Olga Suboč |
| author_facet | Raimondas Čiegis Olga Suboč |
| author_sort | Raimondas Čiegis |
| collection | DOAJ |
| description |
The accuracy of one adaptive integration algorithm is investigated. The accuracy of the discretization is estimated by comparing the discrete and exact stability factors. It is proved that the classical stiffness definition is sufficient for explicit schemes. The complexity of implicit schemes depends on the distribution of eigenvalues of the systems matrix and the information about minimal and maximal values of eigenvalues is not sufficient. Results of numerical experiments are presented.
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| format | Article |
| id | doaj-art-398059c7d1e545c686ba001208f41628 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 1999-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-398059c7d1e545c686ba001208f416282025-02-11T18:15:13ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X1999-12-0139III10.15388/LMD.1999.35670Adaptive integration algorithm for stiff ordinary differential equationsRaimondas Čiegis0Olga Suboč1Vilnius Gediminas Technical UniversityVilnius Gediminas Technical University The accuracy of one adaptive integration algorithm is investigated. The accuracy of the discretization is estimated by comparing the discrete and exact stability factors. It is proved that the classical stiffness definition is sufficient for explicit schemes. The complexity of implicit schemes depends on the distribution of eigenvalues of the systems matrix and the information about minimal and maximal values of eigenvalues is not sufficient. Results of numerical experiments are presented. https://www.zurnalai.vu.lt/LMR/article/view/35670 |
| spellingShingle | Raimondas Čiegis Olga Suboč Adaptive integration algorithm for stiff ordinary differential equations Lietuvos Matematikos Rinkinys |
| title | Adaptive integration algorithm for stiff ordinary differential equations |
| title_full | Adaptive integration algorithm for stiff ordinary differential equations |
| title_fullStr | Adaptive integration algorithm for stiff ordinary differential equations |
| title_full_unstemmed | Adaptive integration algorithm for stiff ordinary differential equations |
| title_short | Adaptive integration algorithm for stiff ordinary differential equations |
| title_sort | adaptive integration algorithm for stiff ordinary differential equations |
| url | https://www.zurnalai.vu.lt/LMR/article/view/35670 |
| work_keys_str_mv | AT raimondasciegis adaptiveintegrationalgorithmforstiffordinarydifferentialequations AT olgasuboc adaptiveintegrationalgorithmforstiffordinarydifferentialequations |