Numerical methods for evolutionary differential equations:
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differen...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
2008
|
| Schriftenreihe: | Computational science and engineering
5 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Zusammenfassung: | Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method |
| Beschreibung: | 1 Online-Ressource (xiii, 395 Seiten) digital file |
| ISBN: | 9780898718911 |
| DOI: | 10.1137/1.9780898718911 |
Internformat
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:20:49Z |
| institution | BVB |
| isbn | 9780898718911 |
| language | English |
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| publishDate | 2008 |
| publishDateSearch | 2008 |
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| spelling | Ascher, Uri M. 1946- (DE-588)136140823 aut Numerical methods for evolutionary differential equations Uri M. Ascher Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 2008 1 Online-Ressource (xiii, 395 Seiten) digital file txt rdacontent c rdamedia cr rdacarrier Computational science and engineering 5 Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method Evolution equations / Numerical solutions Zeitabhängigkeit (DE-588)4320088-6 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Zeitabhängigkeit (DE-588)4320088-6 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Society for Industrial and Applied Mathematics Sonstige oth Computational science and engineering 5 (DE-604)BV040633113 5 https://doi.org/10.1137/1.9780898718911 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ascher, Uri M. 1946- Numerical methods for evolutionary differential equations Computational science and engineering Evolution equations / Numerical solutions Zeitabhängigkeit (DE-588)4320088-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4320088-6 (DE-588)4128130-5 (DE-588)4012249-9 |
| title | Numerical methods for evolutionary differential equations |
| title_auth | Numerical methods for evolutionary differential equations |
| title_exact_search | Numerical methods for evolutionary differential equations |
| title_full | Numerical methods for evolutionary differential equations Uri M. Ascher |
| title_fullStr | Numerical methods for evolutionary differential equations Uri M. Ascher |
| title_full_unstemmed | Numerical methods for evolutionary differential equations Uri M. Ascher |
| title_short | Numerical methods for evolutionary differential equations |
| title_sort | numerical methods for evolutionary differential equations |
| topic | Evolution equations / Numerical solutions Zeitabhängigkeit (DE-588)4320088-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Evolution equations / Numerical solutions Zeitabhängigkeit Numerisches Verfahren Differentialgleichung |
| url | https://doi.org/10.1137/1.9780898718911 |
| volume_link | (DE-604)BV040633113 |
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