High Order Difference Methods for Time Dependent PDE

• Κύριος συγγραφέας: Gustafsson, Bertil (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Σειρά: Springer Series in Computational Mathematics, 38
• Θέματα: Mathematics.; Partial differential equations.; Computer mathematics.; Computational Mathematics and Numerical Analysis.; Partial Differential Equations.

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...

Πίνακας περιεχομένων:

• 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.