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...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
1995
|
| Series: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1995,17 |
| Subjects: | |
| Summary: | 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." |
| Physical Description: | 11 S. |
Staff View
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| 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 | |
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| 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 | |
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| author | Hoffmann, W. Swart, J. J. de |
| author_facet | Hoffmann, W. Swart, J. J. de |
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| 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 |
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| 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 |