Optimally stable fifth-order integration methods: a numerical approach
In this paper, the results of the first detailed and systematic study of the family of fifth order implicit linear multistep methods requiring function evaluations at four backpoints are given. Also described is a practical and efficient nonlinear optimization procedure which made it possible to loc...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000344 |
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| _version_ | 1832554628156227584 |
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| author | D. J. Rodabaugh S. Thompson |
| author_facet | D. J. Rodabaugh S. Thompson |
| author_sort | D. J. Rodabaugh |
| collection | DOAJ |
| description | In this paper, the results of the first detailed and systematic study of the family of fifth order implicit linear multistep methods requiring function evaluations at four backpoints are given. Also described is a practical and efficient nonlinear optimization procedure which made it possible to locate in a precise manner the methods of this type which possess optimal ranges of relative stability in the sense-that the corresponding relative stability regions contain maximal disks centered at the origin. |
| format | Article |
| id | doaj-art-3cea4cfb2f864b5ea98e81fbc439cc57 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3cea4cfb2f864b5ea98e81fbc439cc572025-02-03T05:51:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011331933410.1155/S0161171278000344Optimally stable fifth-order integration methods: a numerical approachD. J. Rodabaugh0S. Thompson1Department of Mathematics, University of Missouri, Columbia 65201, Missouri, USAThe Babcock & Wilcox Company, Nuclear Power Generation Division, Lynchburg 24505, Virginia, USAIn this paper, the results of the first detailed and systematic study of the family of fifth order implicit linear multistep methods requiring function evaluations at four backpoints are given. Also described is a practical and efficient nonlinear optimization procedure which made it possible to locate in a precise manner the methods of this type which possess optimal ranges of relative stability in the sense-that the corresponding relative stability regions contain maximal disks centered at the origin.http://dx.doi.org/10.1155/S0161171278000344linear multistep methodsnumerical solution of ordinary differential equationsrelative stability. |
| spellingShingle | D. J. Rodabaugh S. Thompson Optimally stable fifth-order integration methods: a numerical approach International Journal of Mathematics and Mathematical Sciences linear multistep methods numerical solution of ordinary differential equations relative stability. |
| title | Optimally stable fifth-order integration methods: a numerical
approach |
| title_full | Optimally stable fifth-order integration methods: a numerical
approach |
| title_fullStr | Optimally stable fifth-order integration methods: a numerical
approach |
| title_full_unstemmed | Optimally stable fifth-order integration methods: a numerical
approach |
| title_short | Optimally stable fifth-order integration methods: a numerical
approach |
| title_sort | optimally stable fifth order integration methods a numerical approach |
| topic | linear multistep methods numerical solution of ordinary differential equations relative stability. |
| url | http://dx.doi.org/10.1155/S0161171278000344 |
| work_keys_str_mv | AT djrodabaugh optimallystablefifthorderintegrationmethodsanumericalapproach AT sthompson optimallystablefifthorderintegrationmethodsanumericalapproach |