High Order Difference Methods for Time Dependent PDE: 38 - Brossura
Libro 13 di 33: Springer Computational Mathematics
Sinossi
Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de?nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ?ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful?lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And ?nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial–boundary value problems. The content of the book is not purely theoretical, neither is it a set of recipes for varioustypesof applications. The idea is to give an overviewof the basic theoryand constructionprinciplesfor differencemethodswithoutgoing into all details. For - ample, certain theorems are presented, but the proofs are in most cases left out. The explanation and application of the theory is illustrated by using simple model - amples.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
From the reviews:
"This book presents the theory and construction principles of high order finite difference methods (FDM) for numerical solving of time dependent partial differential equations. ... Many types of finite difference schemes are completely studied and numerical experiments and graphs are presented. ... The book is written in a clear and comprehensive manner. It is recommended to researchers, PD students and readers interested in effective methods for numerical solving of partial differential equations." (Snezhana Gocheva-Ilieva, Zentralblatt MATH, Vol. 1146, 2008)
Contenuti
When are High Order Methods Effective?.- Well-posedness and Stability.- Order of Accuracy and the Convergence Rate.- Approximation in Space.- Approximation in Time.- Coupled Space-Time Approximations.- Boundary Treatment.- The Box Scheme.- Wave Propagation.- A Problem in Fluid Dynamics.- Nonlinear Problems with Shocks.- to Other Numerical Methods.
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High Order Difference Methods for Time Dependent PDE
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Many books have been written on nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial-boundary value problems. The content of the book is not purely theoretical, neither is it a set of recipes for varioustypesof applications. The idea is to give an overviewof the basic theoryand constructionprinciplesfor differencemethodswithoutgoing into all details. For - ample, certain theorems are presented, but the proofs are in most cases left out. The explanation and application of the theory is illustrated by using simple model - amples. 352 pp. Englisch. Codice articolo 9783642094392
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for we. Codice articolo 5048450
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Taschenbuch. Condizione: Neu. High Order Difference Methods for Time Dependent PDE | Bertil Gustafsson | Taschenbuch | Springer Series in Computational Mathematics | xvi | Englisch | 2010 | Springer | EAN 9783642094392 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 107176041
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Many books have been written on nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial¿boundary value problems. The content of the book is not purely theoretical, neither is it a set of recipes for varioustypesof applications. The idea is to give an overviewof the basic theoryand constructionprinciplesfor differencemethodswithoutgoing into all details. For - ample, certain theorems are presented, but the proofs are in most cases left out. The explanation and application of the theory is illustrated by using simple model - amples.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 352 pp. Englisch. Codice articolo 9783642094392
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Many books have been written on nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial-boundary value problems. The content of the book is not purely theoretical, neither is it a set of recipes for varioustypesof applications. The idea is to give an overviewof the basic theoryand constructionprinciplesfor differencemethodswithoutgoing into all details. For - ample, certain theorems are presented, but the proofs are in most cases left out. The explanation and application of the theory is illustrated by using simple model - amples. Codice articolo 9783642094392
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