High Order Difference Methods for Time Dependent PDE

• Main Author: Gustafsson, Bertil (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Springer Series in Computational Mathematics, 38
• Subjects: 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...

Table of Contents:

• 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.