Analysis of Discretization Methods for Ordinary Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Schriftenreihe: | Springer Tracts in Natural Philosophy
23 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finitedifference methods have been known for a long time, their wide applicability and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P. |
| Beschreibung: | 1 Online-Ressource (XVI, 390 p) |
| ISBN: | 9783642654718 9783642654732 |
| ISSN: | 0081-3877 |
| DOI: | 10.1007/978-3-642-65471-8 |
Internformat
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| 500 | |a Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finitedifference methods have been known for a long time, their wide applicability and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P. | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65471-8 |
| format | Electronic eBook |
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| isbn | 9783642654718 9783642654732 |
| issn | 0081-3877 |
| language | English |
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| spelling | Stetter, Hans J. Verfasser aut Analysis of Discretization Methods for Ordinary Differential Equations by Hans J. Stetter Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (XVI, 390 p) txt rdacontent c rdamedia cr rdacarrier Springer Tracts in Natural Philosophy 23 0081-3877 Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finitedifference methods have been known for a long time, their wide applicability and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P. Mathematics Global analysis (Mathematics) Differential Equations Ordinary Differential Equations Analysis Mathematik Diskretisierung (DE-588)4012469-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Diskretisierung (DE-588)4012469-1 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Springer Tracts in Natural Philosophy 23 (DE-604)BV045251612 23 https://doi.org/10.1007/978-3-642-65471-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stetter, Hans J. Analysis of Discretization Methods for Ordinary Differential Equations Springer Tracts in Natural Philosophy Mathematics Global analysis (Mathematics) Differential Equations Ordinary Differential Equations Analysis Mathematik Diskretisierung (DE-588)4012469-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4012469-1 (DE-588)4128130-5 (DE-588)4020929-5 |
| title | Analysis of Discretization Methods for Ordinary Differential Equations |
| title_auth | Analysis of Discretization Methods for Ordinary Differential Equations |
| title_exact_search | Analysis of Discretization Methods for Ordinary Differential Equations |
| title_full | Analysis of Discretization Methods for Ordinary Differential Equations by Hans J. Stetter |
| title_fullStr | Analysis of Discretization Methods for Ordinary Differential Equations by Hans J. Stetter |
| title_full_unstemmed | Analysis of Discretization Methods for Ordinary Differential Equations by Hans J. Stetter |
| title_short | Analysis of Discretization Methods for Ordinary Differential Equations |
| title_sort | analysis of discretization methods for ordinary differential equations |
| topic | Mathematics Global analysis (Mathematics) Differential Equations Ordinary Differential Equations Analysis Mathematik Diskretisierung (DE-588)4012469-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Differential Equations Ordinary Differential Equations Analysis Mathematik Diskretisierung Numerisches Verfahren Gewöhnliche Differentialgleichung |
| url | https://doi.org/10.1007/978-3-642-65471-8 |
| volume_link | (DE-604)BV045251612 |
| work_keys_str_mv | AT stetterhansj analysisofdiscretizationmethodsforordinarydifferentialequations |