B-Series
Algebraic Analysis of Numerical Methods
B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods can be assessed. Runge-Kutta methods, in particular, depend on B-series for a clean and elegant approach to the derivation of high order and efficient methods. However, the utility of B-series goes much further and opens a path to the design and construction of highly accurate and efficient multivalue methods. This book offers a self-contained introduction to B-series by a pioneer of the subject. After…
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Produktdetails
- ISBN: 978-3-030-70955-6
- EAN: 9783030709556
- Produktnummer: 36054101
- Verlag: Springer International Publishing
- Sprache: Englisch
- Erscheinungsjahr: 2021
- Seitenangabe: 320 S.
- Masse: H24.1 cm x B16.0 cm x D2.3 cm 647 g
- Auflage: 1st ed. 2021
- Abbildungen: HC runder Rücken kaschiert
- Gewicht: 647
Über den Autor
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.
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