Butcher-Kuntzmann methods for nonstiff problems on parallel computers:
Abstract: "From a theoretical point of view, the Butcher- Kuntzmann Runge-Kutta methods belong to the best step-by-step methods available in the literature. These methods integrate first-order initial- value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1993
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1993,5 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "From a theoretical point of view, the Butcher- Kuntzmann Runge-Kutta methods belong to the best step-by-step methods available in the literature. These methods integrate first-order initial- value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points. Like the IVP itself, they only need the given initial value without requiring additional starting values, and therefore are a natural discretization of the initial-value problem. On the other hand, from a practical point of view, these methods have the drawback of requiring in each step an approximation to the solution of a system of equations of dimension sd, s and d being the number of stages and the dimension of the initial-value problem, respectively However, parallel computers have changed the scene and enable us to design parallel iteration methods for approximating the solution of the implicit systems such that the Butcher-Kuntzmann methods become efficient step-by-step methods for integrating initial-value problems. In this contribution, we address nonstiff initial-value problems and we investigate the possibility of introducing preconditioners into the iteration method. In particular, the iteration error will be analysed. By a number of numerical experiments it will be shown that the Butcher- Kuntzmann method, in combination with the preconditioned, parallel iteration scheme, performs much more efficient [sic] than the best sequential methods. |
| Beschreibung: | 17 S. |
Internformat
MARC
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| 100 | 1 | |a Houwen, Pieter J. van der |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Butcher-Kuntzmann methods for nonstiff problems on parallel computers |c P. J. van der Houwen ; B. P. Sommeijer |
| 264 | 1 | |a Amsterdam |c 1993 | |
| 300 | |a 17 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1993,5 | |
| 520 | 3 | |a Abstract: "From a theoretical point of view, the Butcher- Kuntzmann Runge-Kutta methods belong to the best step-by-step methods available in the literature. These methods integrate first-order initial- value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points. Like the IVP itself, they only need the given initial value without requiring additional starting values, and therefore are a natural discretization of the initial-value problem. On the other hand, from a practical point of view, these methods have the drawback of requiring in each step an approximation to the solution of a system of equations of dimension sd, s and d being the number of stages and the dimension of the initial-value problem, respectively | |
| 520 | 3 | |a However, parallel computers have changed the scene and enable us to design parallel iteration methods for approximating the solution of the implicit systems such that the Butcher-Kuntzmann methods become efficient step-by-step methods for integrating initial-value problems. In this contribution, we address nonstiff initial-value problems and we investigate the possibility of introducing preconditioners into the iteration method. In particular, the iteration error will be analysed. By a number of numerical experiments it will be shown that the Butcher- Kuntzmann method, in combination with the preconditioned, parallel iteration scheme, performs much more efficient [sic] than the best sequential methods. | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 700 | 1 | |a Sommeijer, Ben P. |d ca. 20. Jh. |e Verfasser |0 (DE-588)132820269 |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1993,5 |w (DE-604)BV010177152 |9 1993,5 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006768264 | ||
Datensatz im Suchindex
| _version_ | 1804124588884361216 |
|---|---|
| any_adam_object | |
| author | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh |
| author_GND | (DE-588)132820269 |
| author_facet | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh |
| author_role | aut aut |
| author_sort | Houwen, Pieter J. van der |
| author_variant | p j v d h pjvd pjvdh b p s bp bps |
| building | Verbundindex |
| bvnumber | BV010187668 |
| ctrlnum | (OCoLC)31389627 (DE-599)BVBBV010187668 |
| format | Book |
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| id | DE-604.BV010187668 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006768264 |
| oclc_num | 31389627 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 17 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Houwen, Pieter J. van der Verfasser aut Butcher-Kuntzmann methods for nonstiff problems on parallel computers P. J. van der Houwen ; B. P. Sommeijer Amsterdam 1993 17 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1993,5 Abstract: "From a theoretical point of view, the Butcher- Kuntzmann Runge-Kutta methods belong to the best step-by-step methods available in the literature. These methods integrate first-order initial- value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points. Like the IVP itself, they only need the given initial value without requiring additional starting values, and therefore are a natural discretization of the initial-value problem. On the other hand, from a practical point of view, these methods have the drawback of requiring in each step an approximation to the solution of a system of equations of dimension sd, s and d being the number of stages and the dimension of the initial-value problem, respectively However, parallel computers have changed the scene and enable us to design parallel iteration methods for approximating the solution of the implicit systems such that the Butcher-Kuntzmann methods become efficient step-by-step methods for integrating initial-value problems. In this contribution, we address nonstiff initial-value problems and we investigate the possibility of introducing preconditioners into the iteration method. In particular, the iteration error will be analysed. By a number of numerical experiments it will be shown that the Butcher- Kuntzmann method, in combination with the preconditioned, parallel iteration scheme, performs much more efficient [sic] than the best sequential methods. Numerical analysis Runge-Kutta formulas Sommeijer, Ben P. ca. 20. Jh. Verfasser (DE-588)132820269 aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1993,5 (DE-604)BV010177152 1993,5 |
| spellingShingle | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh Butcher-Kuntzmann methods for nonstiff problems on parallel computers Numerical analysis Runge-Kutta formulas |
| title | Butcher-Kuntzmann methods for nonstiff problems on parallel computers |
| title_auth | Butcher-Kuntzmann methods for nonstiff problems on parallel computers |
| title_exact_search | Butcher-Kuntzmann methods for nonstiff problems on parallel computers |
| title_full | Butcher-Kuntzmann methods for nonstiff problems on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_fullStr | Butcher-Kuntzmann methods for nonstiff problems on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_full_unstemmed | Butcher-Kuntzmann methods for nonstiff problems on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_short | Butcher-Kuntzmann methods for nonstiff problems on parallel computers |
| title_sort | butcher kuntzmann methods for nonstiff problems on parallel computers |
| topic | Numerical analysis Runge-Kutta formulas |
| topic_facet | Numerical analysis Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT houwenpieterjvander butcherkuntzmannmethodsfornonstiffproblemsonparallelcomputers AT sommeijerbenp butcherkuntzmannmethodsfornonstiffproblemsonparallelcomputers |