Numerical time-dependent partial differential equations for scientists and engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2010
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Mathematics in science and engineering
v. 213 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations Includes bibliographical references (pages 273-287) and index |
| Beschreibung: | 1 Online-Ressource (x, 294 pages) |
| ISBN: | 9780080917047 0080917046 9780121339814 0121339815 |
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| 245 | 1 | 0 | |a Numerical time-dependent partial differential equations for scientists and engineers |c Moysey Brio, Aramais R. Zakharian, Gary M. Webb |
| 250 | |a 1st ed | ||
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| 490 | 0 | |a Mathematics in science and engineering |v v. 213 | |
| 500 | |a It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. | ||
| 500 | |a The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. | ||
| 500 | |a The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations | ||
| 500 | |a Includes bibliographical references (pages 273-287) and index | ||
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Differential Equations / Partial |2 bisacsh | |
| 650 | 7 | |a Differential equations, Partial / Numerical solutions |2 fast | |
| 650 | 7 | |a Numerical analysis |2 fast | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
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Datensatz im Suchindex
| _version_ | 1804152878783266816 |
|---|---|
| any_adam_object | |
| author | Brio, Moysey 1952- |
| author_GND | (DE-588)174033230 (DE-588)1154328066 |
| author_facet | Brio, Moysey 1952- |
| author_role | aut |
| author_sort | Brio, Moysey 1952- |
| author_variant | m b mb |
| building | Verbundindex |
| bvnumber | BV042300886 |
| collection | ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (OCoLC)668208508 (DE-599)BVBBV042300886 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9780080917047 0080917046 9780121339814 0121339815 |
| language | English |
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| spelling | Brio, Moysey 1952- Verfasser (DE-588)174033230 aut Numerical time-dependent partial differential equations for scientists and engineers Moysey Brio, Aramais R. Zakharian, Gary M. Webb 1st ed Amsterdam Elsevier 2010 1 Online-Ressource (x, 294 pages) txt rdacontent c rdamedia cr rdacarrier Mathematics in science and engineering v. 213 It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations Includes bibliographical references (pages 273-287) and index Mathematics MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Partial / Numerical solutions fast Numerical analysis fast Mathematik Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Zeitabhängigkeit (DE-588)4320088-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Zeitabhängigkeit (DE-588)4320088-6 s 1\p DE-604 Webb, Gary Sonstige (DE-588)1154328066 oth Zakharian, Aramais R. Sonstige oth http://www.sciencedirect.com/science/book/9780121339814 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brio, Moysey 1952- Numerical time-dependent partial differential equations for scientists and engineers Mathematics MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Partial / Numerical solutions fast Numerical analysis fast Mathematik Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Zeitabhängigkeit (DE-588)4320088-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4320088-6 |
| title | Numerical time-dependent partial differential equations for scientists and engineers |
| title_auth | Numerical time-dependent partial differential equations for scientists and engineers |
| title_exact_search | Numerical time-dependent partial differential equations for scientists and engineers |
| title_full | Numerical time-dependent partial differential equations for scientists and engineers Moysey Brio, Aramais R. Zakharian, Gary M. Webb |
| title_fullStr | Numerical time-dependent partial differential equations for scientists and engineers Moysey Brio, Aramais R. Zakharian, Gary M. Webb |
| title_full_unstemmed | Numerical time-dependent partial differential equations for scientists and engineers Moysey Brio, Aramais R. Zakharian, Gary M. Webb |
| title_short | Numerical time-dependent partial differential equations for scientists and engineers |
| title_sort | numerical time dependent partial differential equations for scientists and engineers |
| topic | Mathematics MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Partial / Numerical solutions fast Numerical analysis fast Mathematik Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Zeitabhängigkeit (DE-588)4320088-6 gnd |
| topic_facet | Mathematics MATHEMATICS / Differential Equations / Partial Differential equations, Partial / Numerical solutions Numerical analysis Mathematik Differential equations, Partial Numerical solutions Partielle Differentialgleichung Zeitabhängigkeit |
| url | http://www.sciencedirect.com/science/book/9780121339814 |
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