B-Series
Springer International Publishing (Verlag)
978-3-030-70955-6 (ISBN)
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.
John Butcher is recognised as the founder of the modern theory of Runge-Kutta methods and discover of the Butcher group. His contributions to numerical analysis include the formulation of implicit Runge-Kutta methods, particularly methods based on Gauss-Legendre, Radau and Lobatto quadrature, general linear methods, order barriers for explicit Runge-Kutta methods, effective order, non-linear stability and order arrows. His name is attached to the Butcher tableau and the Butcher product, as well as to the Butcher group and Butcher series.
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.
1 Differential equations, numerical methods and algebraic analysis.- 2 Trees and forests.- 3 B-series and algebraic analysis.- 4 Algebraic analysis and integration methods.- 5 B-series and Runge-Kutta methods.- 6 B-series and multivalue methods.- 7 B-series and geometric integration.- Answers to the exercises.- References.- Index.
| Erscheinungsdatum | 08.04.2021 |
|---|---|
| Reihe/Serie | Springer Series in Computational Mathematics |
| Zusatzinfo | X, 310 p. 50 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 637 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Butcher group • Butcher series • forests • Graphs • G-symplectic methods • Multivalue methods • Numerical Methods • ordinary differential equation • Runge-Kutta • Symplectic Methods • Trees |
| ISBN-10 | 3-030-70955-8 / 3030709558 |
| ISBN-13 | 978-3-030-70955-6 / 9783030709556 |
| Zustand | Neuware |
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