Richardson Extrapolation

Zahari Zlatev; Ivan Dimov; István Faragó; Ágnes Havasi

Published by De Gruyter 2018

Richardson Extrapolation

Practical Aspects and Applications

Zahari Zlatev, Ivan Dimov, István Faragó and Ágnes Havasi

Volume 2 in the series De Gruyter Series in Applied and Numerical Mathematics

https://doi.org/10.1515/9783110533002

Overview
Contents

About this book

Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book.
Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations.

Contents
The basic properties of Richardson extrapolation
Richardson extrapolation for explicit Runge-Kutta methods
Linear multistep and predictor-corrector methods
Richardson extrapolation for some implicit methods
Richardson extrapolation for splitting techniques
Richardson extrapolation for advection problems
Richardson extrapolation for some other problems
General conclusions

The first comprehensive treatment of the theory and applications of Richardson extrapolation
Discusses in detail the stability issues of the method
Includes concrete worked out examples and applications

Author information

Z. Zlatev, Aarhus Univ., Denmark; I. Dimov, Bulgarian Acad. of Sci., Bulgaria; I. Faragó and Á. Havasi, Eötvös Loránd Univ., Hungary.

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	xiii
1. The basic properties of Richardson extrapolation Requires Authentication Unlicensed Licensed Download PDF	1
2. Richardson extrapolation for explicit Runge–Kutta methods Requires Authentication Unlicensed Licensed Download PDF	23
3. Linear multistep and predictor-corrector methods Requires Authentication Unlicensed Licensed Download PDF	75
4. Richardson extrapolation for some implicit methods Requires Authentication Unlicensed Licensed Download PDF	119
5.2 Richardson extrapolation for splitting techniques Requires Authentication Unlicensed Licensed Download PDF	181
6. Richardson extrapolation for advection problems Requires Authentication Unlicensed Licensed Download PDF	215
7. Richardson extrapolation for some other problems Requires Authentication Unlicensed Licensed Download PDF	257
8. General conclusions Requires Authentication Unlicensed Licensed Download PDF	277
References Requires Authentication Unlicensed Licensed Download PDF	279
List of abbreviations Requires Authentication Unlicensed Licensed Download PDF	287
Author index Requires Authentication Unlicensed Licensed Download PDF	289
Subject index Requires Authentication Unlicensed Licensed Download PDF	291

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematics, physics, and engineering.
Pages
- Front matter: 17
- Main content: 292
Illustrations
- Illustrations: 22
- Coloured Illustrations: 16
- Tables: 73
Keywords: Extrapolation; Differentialgleichung; Numerisches Verfahren; Operator-Splitting-Verfahren; Runge-Kutta-Verfahren

eBook

Published: November 7, 2017
ISBN: 9783110533002

Hardcover

Published: November 7, 2017
ISBN: 9783110516494

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Richardson Extrapolation

Practical Aspects and Applications