Iteration of Runge Kutta methods with block triangular Jacobians:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
1995
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1995,6 |
| Schlagwörter: | |
| Abstract: | Abstract: "We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Jacobian. For IVPs of large dimension, this approach is not attractive because of the high costs involved in the LU-decomposition of the Jacobian of the RK equations. Several proposals have been made to reduce these high costs. The most well-known remedy is the use of similarity transformations by which the RK Jacobian is transformed to a block-diagonal matrix whose blocks have the IVP dimension. In this paper we study an alternative approach which directly replaces the RK Jacobian by a block-diagonal or block-triangular matrix whose blocks themselves are block-triangular matrices. Such a grossly 'simplified' Newton iteration process allows for a considerable amount of parallelism. However, the important issue is whether this block-triangular approach does converge. It is the aim of this paper to get insight into the effect on the convergence of block-triangular Jacobian approximations." |
| Umfang: | 16 S. |
Internformat
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| 049 | |a DE-91G | ||
| 100 | 1 | |a Houwen, Pieter J. van der |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Iteration of Runge Kutta methods with block triangular Jacobians |c P. J. van der Houwen ; B. P. Sommeijer |
| 264 | 1 | |a Amsterdam |c 1995 | |
| 300 | |a 16 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 1995,6 | |
| 520 | 3 | |a Abstract: "We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Jacobian. For IVPs of large dimension, this approach is not attractive because of the high costs involved in the LU-decomposition of the Jacobian of the RK equations. Several proposals have been made to reduce these high costs. The most well-known remedy is the use of similarity transformations by which the RK Jacobian is transformed to a block-diagonal matrix whose blocks have the IVP dimension. In this paper we study an alternative approach which directly replaces the RK Jacobian by a block-diagonal or block-triangular matrix whose blocks themselves are block-triangular matrices. Such a grossly 'simplified' Newton iteration process allows for a considerable amount of parallelism. However, the important issue is whether this block-triangular approach does converge. It is the aim of this paper to get insight into the effect on the convergence of block-triangular Jacobian approximations." | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Initial value problems | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
| 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 1995,6 |w (DE-604)BV010177152 |9 1995,6 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007406884 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0111 2001 B 6003-1995,6 |
|---|---|
| DE-BY-TUM_katkey | 775376 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010456656 |
| _version_ | 1821938649779929088 |
| 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 | BV011059627 |
| ctrlnum | (OCoLC)34740293 (DE-599)BVBBV011059627 |
| format | Book |
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| id | DE-604.BV011059627 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:05:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007406884 |
| oclc_num | 34740293 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 16 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spellingShingle | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh Iteration of Runge Kutta methods with block triangular Jacobians Algorithms Initial value problems Iterative methods (Mathematics) Runge-Kutta formulas |
| title | Iteration of Runge Kutta methods with block triangular Jacobians |
| title_auth | Iteration of Runge Kutta methods with block triangular Jacobians |
| title_exact_search | Iteration of Runge Kutta methods with block triangular Jacobians |
| title_full | Iteration of Runge Kutta methods with block triangular Jacobians P. J. van der Houwen ; B. P. Sommeijer |
| title_fullStr | Iteration of Runge Kutta methods with block triangular Jacobians P. J. van der Houwen ; B. P. Sommeijer |
| title_full_unstemmed | Iteration of Runge Kutta methods with block triangular Jacobians P. J. van der Houwen ; B. P. Sommeijer |
| title_short | Iteration of Runge Kutta methods with block triangular Jacobians |
| title_sort | iteration of runge kutta methods with block triangular jacobians |
| topic | Algorithms Initial value problems Iterative methods (Mathematics) Runge-Kutta formulas |
| topic_facet | Algorithms Initial value problems Iterative methods (Mathematics) Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT houwenpieterjvander iterationofrungekuttamethodswithblocktriangularjacobians AT sommeijerbenp iterationofrungekuttamethodswithblocktriangularjacobians |
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik, Berichte
| Signatur: |
0111 2001 B 6003-1995,6 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |