Surveys in Applied Mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1995
|
| Schriftenreihe: | Surveys in Applied Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity |
| Beschreibung: | 1 Online-Ressource (XII, 264 p) |
| ISBN: | 9781489904362 9781489904386 |
| DOI: | 10.1007/978-1-4899-0436-2 |
Internformat
MARC
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| 245 | 1 | 0 | |a Surveys in Applied Mathematics |c edited by Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou |
| 264 | 1 | |a Boston, MA |b Springer US |c 1995 | |
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| 490 | 0 | |a Surveys in Applied Mathematics | |
| 500 | |a Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a McLaughlin, David W. |e Sonstige |0 (DE-588)1067165444 |4 oth | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Keller, Joseph B. 1923-2016 |
| author_GND | (DE-588)174171366 (DE-588)1067165444 (DE-588)171732456 |
| author_facet | Keller, Joseph B. 1923-2016 |
| author_role | aut |
| author_sort | Keller, Joseph B. 1923-2016 |
| author_variant | j b k jb jbk |
| building | Verbundindex |
| bvnumber | BV042421744 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)867210122 (DE-599)BVBBV042421744 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4899-0436-2 |
| format | Electronic eBook |
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| id | DE-604.BV042421744 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781489904362 9781489904386 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857161 |
| oclc_num | 867210122 |
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| physical | 1 Online-Ressource (XII, 264 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer US |
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| series2 | Surveys in Applied Mathematics |
| spelling | Keller, Joseph B. 1923-2016 Verfasser (DE-588)174171366 aut Surveys in Applied Mathematics edited by Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou Boston, MA Springer US 1995 1 Online-Ressource (XII, 264 p) txt rdacontent c rdamedia cr rdacarrier Surveys in Applied Mathematics Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity Mathematics Differential equations, partial Applications of Mathematics Partial Differential Equations Mathematik McLaughlin, David W. Sonstige (DE-588)1067165444 oth Papanicolaou, George 1943- Sonstige (DE-588)171732456 oth https://doi.org/10.1007/978-1-4899-0436-2 Verlag Volltext |
| spellingShingle | Keller, Joseph B. 1923-2016 Surveys in Applied Mathematics Mathematics Differential equations, partial Applications of Mathematics Partial Differential Equations Mathematik |
| title | Surveys in Applied Mathematics |
| title_auth | Surveys in Applied Mathematics |
| title_exact_search | Surveys in Applied Mathematics |
| title_full | Surveys in Applied Mathematics edited by Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou |
| title_fullStr | Surveys in Applied Mathematics edited by Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou |
| title_full_unstemmed | Surveys in Applied Mathematics edited by Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou |
| title_short | Surveys in Applied Mathematics |
| title_sort | surveys in applied mathematics |
| topic | Mathematics Differential equations, partial Applications of Mathematics Partial Differential Equations Mathematik |
| topic_facet | Mathematics Differential equations, partial Applications of Mathematics Partial Differential Equations Mathematik |
| url | https://doi.org/10.1007/978-1-4899-0436-2 |
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