High Order Difference Methods for Time Dependent PDE by Bertil Gustafsson
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.-
Numerical Analysis for Elliptic Optimal Control Problems
-
Introduction to Shape Optimization
-
Numerical Methods for Two-phase Incompressible Flows
-
Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
-
Spectral Methods
-
The Graduate Student's Guide to Numerical Analysis '98
-
The Linearization Method for Constrained Optimization
-
Hilbert Space Splittings and Iterative Methods
-
The Concept of Stability in Numerical Mathematics
-
Monotone Discretizations for Elliptic Second Order Partial Differential Equations
-
Boundary Element Methods
-
History of Continued Fractions and Padé Approximants
-
Method of Difference Potentials and Its Applications
-
Newton Methods for Nonlinear Problems
-
Logarithmic Norms
-
Minimization Methods for Non-Differentiable Functions
-
Numerical Toolbox for Verified Computing I
-
Hierarchical Matrices: Algorithms and Analysis
-
Mixed and Hybrid Finite Element Methods
-
Solving Elliptic Problems Using ELLPACK
-
Discrete Iterations
-
Numerical Techniques for Stochastic Optimization
-
Numerical Continuation Methods
-
Krylov Methods for Nonsymmetric Linear Systems
-
Progress in Approximation Theory
-
Sequence Transformations
-
Nonlinear Approximation Theory
-
Moduli of Smoothness
-
Numerical Methods Based on Sinc and Analytic Functions
-
Krylov Subspace Methods for Linear Systems
-
Advanced Boundary Element Methods
-
Retarded Potentials and Time Domain Boundary Integral Equations
-
Numerical Modeling in Materials Science and Engineering
-
Robust Numerical Methods for Singularly Perturbed Differential Equations
-
Finite Element Methods for Incompressible Flow Problems
-
Solving Ordinary Differential Equations I
-
Solving Ordinary Differential Equations II
-
Tensor Spaces and Numerical Tensor Calculus
-
Matrix Iterative Analysis
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)
| SKU | Unavailable |
| ISBN 13 | 9783540749929 |
| ISBN 10 | 3540749926 |
| Title | High Order Difference Methods for Time Dependent PDE |
| Author | Bertil Gustafsson |
| Series | Springer Series In Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer |
| Year published | 2007-12-07 |
| Number of pages | 334 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |