Approximating Runge Kutta matrices by triangular matrices:
Abstract: "The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1995
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1995,17 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit iteration methods for ODE-IVP solvers [HSw95] substitute the Runge-Kutta matrix A in the Newton process for a triangular matrix T that approximates A, hereby making the method suitable for parallel implementation. The matrix T is constructed according to a simple procedure, such that the stiff error components in the numerical solution are strongly damped. In this paper we prove for a large class of Runge- Kutta methods that this procedure can be carried out and that the diagonal entries of T are positive. This means that the linear systems that are to be solved have a non-singular matrix." |
| Beschreibung: | 11 S. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011033272 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 961104s1995 |||| 00||| engod | ||
| 035 | |a (OCoLC)35448366 | ||
| 035 | |a (DE-599)BVBBV011033272 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G | ||
| 100 | 1 | |a Hoffmann, W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Approximating Runge Kutta matrices by triangular matrices |c W. Hoffmann ; J. J. B. de Swart |
| 264 | 1 | |a Amsterdam |c 1995 | |
| 300 | |a 11 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 1995,17 | |
| 520 | 3 | |a Abstract: "The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit iteration methods for ODE-IVP solvers [HSw95] substitute the Runge-Kutta matrix A in the Newton process for a triangular matrix T that approximates A, hereby making the method suitable for parallel implementation. The matrix T is constructed according to a simple procedure, such that the stiff error components in the numerical solution are strongly damped. In this paper we prove for a large class of Runge- Kutta methods that this procedure can be carried out and that the diagonal entries of T are positive. This means that the linear systems that are to be solved have a non-singular matrix." | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 700 | 1 | |a Swart, J. J. de |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1995,17 |w (DE-604)BV010177152 |9 1995,17 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007388194 | ||
Datensatz im Suchindex
| _version_ | 1804125523792625664 |
|---|---|
| any_adam_object | |
| author | Hoffmann, W. Swart, J. J. de |
| author_facet | Hoffmann, W. Swart, J. J. de |
| author_role | aut aut |
| author_sort | Hoffmann, W. |
| author_variant | w h wh j j d s jjd jjds |
| building | Verbundindex |
| bvnumber | BV011033272 |
| ctrlnum | (OCoLC)35448366 (DE-599)BVBBV011033272 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01944nam a2200313 cb4500</leader><controlfield tag="001">BV011033272</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">961104s1995 |||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)35448366</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011033272</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hoffmann, W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximating Runge Kutta matrices by triangular matrices</subfield><subfield code="c">W. Hoffmann ; J. J. B. de Swart</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">11 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM</subfield><subfield code="v">1995,17</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit iteration methods for ODE-IVP solvers [HSw95] substitute the Runge-Kutta matrix A in the Newton process for a triangular matrix T that approximates A, hereby making the method suitable for parallel implementation. The matrix T is constructed according to a simple procedure, such that the stiff error components in the numerical solution are strongly damped. In this paper we prove for a large class of Runge- Kutta methods that this procedure can be carried out and that the diagonal entries of T are positive. This means that the linear systems that are to be solved have a non-singular matrix."</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrices</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Runge-Kutta formulas</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Swart, J. J. de</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Afdeling Numerieke Wiskunde: Report NM</subfield><subfield code="t">Centrum voor Wiskunde en Informatica <Amsterdam></subfield><subfield code="v">1995,17</subfield><subfield code="w">(DE-604)BV010177152</subfield><subfield code="9">1995,17</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007388194</subfield></datafield></record></collection> |
| id | DE-604.BV011033272 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:02:55Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007388194 |
| oclc_num | 35448366 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 11 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Hoffmann, W. Verfasser aut Approximating Runge Kutta matrices by triangular matrices W. Hoffmann ; J. J. B. de Swart Amsterdam 1995 11 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1995,17 Abstract: "The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently proposed triangularly implicit iteration methods for ODE-IVP solvers [HSw95] substitute the Runge-Kutta matrix A in the Newton process for a triangular matrix T that approximates A, hereby making the method suitable for parallel implementation. The matrix T is constructed according to a simple procedure, such that the stiff error components in the numerical solution are strongly damped. In this paper we prove for a large class of Runge- Kutta methods that this procedure can be carried out and that the diagonal entries of T are positive. This means that the linear systems that are to be solved have a non-singular matrix." Matrices Runge-Kutta formulas Swart, J. J. de Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1995,17 (DE-604)BV010177152 1995,17 |
| spellingShingle | Hoffmann, W. Swart, J. J. de Approximating Runge Kutta matrices by triangular matrices Matrices Runge-Kutta formulas |
| title | Approximating Runge Kutta matrices by triangular matrices |
| title_auth | Approximating Runge Kutta matrices by triangular matrices |
| title_exact_search | Approximating Runge Kutta matrices by triangular matrices |
| title_full | Approximating Runge Kutta matrices by triangular matrices W. Hoffmann ; J. J. B. de Swart |
| title_fullStr | Approximating Runge Kutta matrices by triangular matrices W. Hoffmann ; J. J. B. de Swart |
| title_full_unstemmed | Approximating Runge Kutta matrices by triangular matrices W. Hoffmann ; J. J. B. de Swart |
| title_short | Approximating Runge Kutta matrices by triangular matrices |
| title_sort | approximating runge kutta matrices by triangular matrices |
| topic | Matrices Runge-Kutta formulas |
| topic_facet | Matrices Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT hoffmannw approximatingrungekuttamatricesbytriangularmatrices AT swartjjde approximatingrungekuttamatricesbytriangularmatrices |