Similarity Methods for Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1974
|
| Schriftenreihe: | Applied Mathematical Sciences
13 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of transformations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation |
| Beschreibung: | 1 Online-Ressource (IX, 333 p) |
| ISBN: | 9781461263944 9780387901077 |
| DOI: | 10.1007/978-1-4612-6394-4 |
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| 490 | 1 | |a Applied Mathematical Sciences |v 13 | |
| 500 | |a The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of transformations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation | ||
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-6394-4 |
| format | Electronic eBook |
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| id | DE-604.BV042420480 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461263944 9780387901077 |
| language | English |
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| spelling | Bluman, G. W. Verfasser aut Similarity Methods for Differential Equations by G. W. Bluman, J. D. Cole New York, NY Springer New York 1974 1 Online-Ressource (IX, 333 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 13 The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of transformations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation Mathematics Mathematics, general Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Cole, J. D. Sonstige oth Applied Mathematical Sciences 13 (DE-604)BV040244599 13 https://doi.org/10.1007/978-1-4612-6394-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bluman, G. W. Similarity Methods for Differential Equations Applied Mathematical Sciences Mathematics Mathematics, general Mathematik Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Similarity Methods for Differential Equations |
| title_auth | Similarity Methods for Differential Equations |
| title_exact_search | Similarity Methods for Differential Equations |
| title_full | Similarity Methods for Differential Equations by G. W. Bluman, J. D. Cole |
| title_fullStr | Similarity Methods for Differential Equations by G. W. Bluman, J. D. Cole |
| title_full_unstemmed | Similarity Methods for Differential Equations by G. W. Bluman, J. D. Cole |
| title_short | Similarity Methods for Differential Equations |
| title_sort | similarity methods for differential equations |
| topic | Mathematics Mathematics, general Mathematik Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-6394-4 |
| volume_link | (DE-604)BV040244599 |
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