The development of Runge-Kutta methods for partial differential equations:
Abstract: "A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is the Method of Lines. This method transforms the PDE into a system of ordinary differential equations (ODEs) by discretization of the space variables an...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1994
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1994,20 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is the Method of Lines. This method transforms the PDE into a system of ordinary differential equations (ODEs) by discretization of the space variables and uses an ODE solver for the time integration. Since ODEs originating from space-discretized PDEs have a special structure, not every ODE solver is appropriate. For example, the well-known fourth-order Runge-Kutta method is highly inefficient if the PDE is parabolic, but it performs often quite satisfactory [sic] if the PDE is hyperbolic. In this lecture, we give a survey of the development of ODE methods that are tuned to space-discretized PDEs. Because of the overwhelming number of methods that have been proposed through the years, we confine our considerations to Runge-Kutta type methods. In this contribution to this historical surveys presented at the IMACS 14 World Congress held in July 1994 in Atlanta, we describe work of Crank and Nicolson (1947), Laasonen (1949), Peaceman and Rachford (1955), Yuan' Chzao-Din (1958), Stiefel (1958), Franklin (1959), Guillou & Lago (1960), Metzger (1967), Lomax (1968), Gourlay (1970), Riha (1972), Gentzch and Schlüter (1978), Vichnevetsky (1983), Kinnmark and Gray (1984), Sonneveld and van Leer (1985), as well as research carried out at CWI." |
| Beschreibung: | 15 S. |
Internformat
MARC
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| 100 | 1 | |a Houwen, Pieter J. van der |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The development of Runge-Kutta methods for partial differential equations |c P. J. van der Houwen |
| 264 | 1 | |a Amsterdam |c 1994 | |
| 300 | |a 15 S. | ||
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| 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 1994,20 | |
| 520 | 3 | |a Abstract: "A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is the Method of Lines. This method transforms the PDE into a system of ordinary differential equations (ODEs) by discretization of the space variables and uses an ODE solver for the time integration. Since ODEs originating from space-discretized PDEs have a special structure, not every ODE solver is appropriate. For example, the well-known fourth-order Runge-Kutta method is highly inefficient if the PDE is parabolic, but it performs often quite satisfactory [sic] if the PDE is hyperbolic. In this lecture, we give a survey of the development of ODE methods that are tuned to space-discretized PDEs. Because of the overwhelming number of methods that have been proposed through the years, we confine our considerations to Runge-Kutta type methods. In this contribution to this historical surveys presented at the IMACS 14 World Congress held in July 1994 in Atlanta, we describe work of Crank and Nicolson (1947), Laasonen (1949), Peaceman and Rachford (1955), Yuan' Chzao-Din (1958), Stiefel (1958), Franklin (1959), Guillou & Lago (1960), Metzger (1967), Lomax (1968), Gourlay (1970), Riha (1972), Gentzch and Schlüter (1978), Vichnevetsky (1983), Kinnmark and Gray (1984), Sonneveld and van Leer (1985), as well as research carried out at CWI." | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1994,20 |w (DE-604)BV010177152 |9 1994,20 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006768986 | ||
Datensatz im Suchindex
| _version_ | 1804124590058766336 |
|---|---|
| any_adam_object | |
| author | Houwen, Pieter J. van der |
| author_facet | Houwen, Pieter J. van der |
| author_role | aut |
| author_sort | Houwen, Pieter J. van der |
| author_variant | p j v d h pjvd pjvdh |
| building | Verbundindex |
| bvnumber | BV010188478 |
| ctrlnum | (OCoLC)32904754 (DE-599)BVBBV010188478 |
| format | Book |
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| id | DE-604.BV010188478 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:05Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006768986 |
| oclc_num | 32904754 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 15 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Houwen, Pieter J. van der Verfasser aut The development of Runge-Kutta methods for partial differential equations P. J. van der Houwen Amsterdam 1994 15 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1994,20 Abstract: "A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is the Method of Lines. This method transforms the PDE into a system of ordinary differential equations (ODEs) by discretization of the space variables and uses an ODE solver for the time integration. Since ODEs originating from space-discretized PDEs have a special structure, not every ODE solver is appropriate. For example, the well-known fourth-order Runge-Kutta method is highly inefficient if the PDE is parabolic, but it performs often quite satisfactory [sic] if the PDE is hyperbolic. In this lecture, we give a survey of the development of ODE methods that are tuned to space-discretized PDEs. Because of the overwhelming number of methods that have been proposed through the years, we confine our considerations to Runge-Kutta type methods. In this contribution to this historical surveys presented at the IMACS 14 World Congress held in July 1994 in Atlanta, we describe work of Crank and Nicolson (1947), Laasonen (1949), Peaceman and Rachford (1955), Yuan' Chzao-Din (1958), Stiefel (1958), Franklin (1959), Guillou & Lago (1960), Metzger (1967), Lomax (1968), Gourlay (1970), Riha (1972), Gentzch and Schlüter (1978), Vichnevetsky (1983), Kinnmark and Gray (1984), Sonneveld and van Leer (1985), as well as research carried out at CWI." Runge-Kutta formulas Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1994,20 (DE-604)BV010177152 1994,20 |
| spellingShingle | Houwen, Pieter J. van der The development of Runge-Kutta methods for partial differential equations Runge-Kutta formulas |
| title | The development of Runge-Kutta methods for partial differential equations |
| title_auth | The development of Runge-Kutta methods for partial differential equations |
| title_exact_search | The development of Runge-Kutta methods for partial differential equations |
| title_full | The development of Runge-Kutta methods for partial differential equations P. J. van der Houwen |
| title_fullStr | The development of Runge-Kutta methods for partial differential equations P. J. van der Houwen |
| title_full_unstemmed | The development of Runge-Kutta methods for partial differential equations P. J. van der Houwen |
| title_short | The development of Runge-Kutta methods for partial differential equations |
| title_sort | the development of runge kutta methods for partial differential equations |
| topic | Runge-Kutta formulas |
| topic_facet | Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT houwenpieterjvander thedevelopmentofrungekuttamethodsforpartialdifferentialequations |