Overview
- A thorough introduction to B-series, written by its originator
- Contains a self-contained analysis of Runge-Kutta methods
- Includes a detailed study of trees and related constructs
- Applies B-series to general linear methods and structure-preserving methods
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 55)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book offers a self-contained introduction to B-series by a pioneer of the subject. After a preliminary chapter providing background on differential equations and numerical methods, a broad exposition of graphs and trees is presented. This is essential preparation for the third chapter, in which the main ideas of B-series are introduced and developed. In chapter four, algebraic aspects are further analysed in the context of integration methods, a generalization of Runge–Kutta methods to infinite index sets. Chapter five, on explicit and implicit Runge–Kutta methods, contrasts the B-series and classical approaches. Chapter six, on multivalue methods, gives a traditional review of linear multistep methods and expands this to general linear methods, for which the B-series approach is both natural and essential. The final chapter introduces some aspects of geometric integration, from a B-series point of view.
Placing B-series at the centre of its most important applications makes this book an invaluable resource for scientists, engineers and mathematicians who depend on computational modelling, not to mention computational scientists who carry out research on numerical methods in differential equations. In addition to exercises with solutions and study notes, a number of open-ended projects are suggested. This combination makes the book ideal as a textbook for specialised courses on numerical methods for differential equations, as well as suitable for self-study.
Authors and Affiliations
About the author
John is a fellow of the New Zealand Mathematical Society, the Royal Society of New Zealand and the Society for Industrial and Applied Mathematics. He is an Officer of the New Zealand Order of Merit and his awards include the Jones Medal of the Royal Society of New Zealand and the Van Wijngaarden Award of the Centrum Wiskunde & Informatica, Amsterdam.
Bibliographic Information
Book Title: B-Series
Book Subtitle: Algebraic Analysis of Numerical Methods
Authors: John C. Butcher
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-030-70956-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-70955-6Published: 02 April 2021
Softcover ISBN: 978-3-030-70958-7Published: 02 April 2022
eBook ISBN: 978-3-030-70956-3Published: 01 April 2021
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: X, 310
Number of Illustrations: 50 b/w illustrations
Topics: Computational Mathematics and Numerical Analysis, Numerical Analysis, Analysis