High Order Difference Methods for Time Dependent PDE

  • Bertil Gustafsson

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 38)

Table of contents

About this book

Introduction

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.

Keywords

Approximation difference methods high order initial-boundary value problems partial differential equation stability wave propagation

Authors and affiliations

  • Bertil Gustafsson
    • 1
  1. 1.UppsalaSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74993-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74992-9
  • Online ISBN 978-3-540-74993-6
  • Series Print ISSN 0179-3632
  • About this book
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