Overview
- Contains articles from highly distinguished experts in numerical analysis
- Offers a unique perspective on modern algebraic and combinatorial structures
- Combines overview and research articles on recent and ongoing developments, as well as new research directions
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 267)
Included in the following conference series:
Conference proceedings info: DMGILBS 2015.
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About this book
This volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions.
Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic andcombinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives.
The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.
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Keywords
- 65D30, 34A26, 15A16, 34C40, 16T05, 70G75
- 37C10, 70G65, 93B25, 17B99, 22E65, 65P10
- Geometric integration
- Lie group integrators
- nonlinear control theory
- Hopf algebras
- Lie groups
- word series
- Chen-Fliess series
- Baker–Campbell–Hausdorff formula
- Magnus expansion
- Discrete Mechanics
- Geometric Integration
- Lie–Butcher Series
Table of contents (11 papers)
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Front Matter
Editors and Affiliations
About the editors
María Barbero Liñán is an associate professor in the department of applied mathematics at Universidad Politécnica de Madrid, Spain. After obtaining her Ph.D. in Applied Mathematics at Universidad Politécnica de Cataluña, she has been postdoctoral researcher at INRIA (Nancy, France), Queen's University (Kingston, ON, Canada), ICMAT and Universidad Carlos III de Madrid in Spain.
Kurusch Ebrahimi-Fard is an associate professor of mathematics in the department of mathematical sciences at the Norwegian University of Science and Technology in Trondheim, Norway. After obtaining his Ph.D. in Theoretical Physics from Bonn University, he has held postdoctoral positions, among others, at the IHES (Bures-Sur-Yvette, France), Max Planck Institute for Mathematics (Bonn, Germany) and the Instituto de Ciencias Matemáticas (Madrid, Spain).
Bibliographic Information
Book Title: Discrete Mechanics, Geometric Integration and Lie–Butcher Series
Book Subtitle: DMGILBS, Madrid, May 2015
Editors: Kurusch Ebrahimi-Fard, María Barbero Liñán
Series Title: Springer Proceedings in Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-030-01397-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-01396-7Published: 05 November 2018
Softcover ISBN: 978-3-030-13177-7Published: 10 December 2019
eBook ISBN: 978-3-030-01397-4Published: 05 November 2018
Series ISSN: 2194-1009
Series E-ISSN: 2194-1017
Edition Number: 1
Number of Pages: X, 361
Number of Illustrations: 166 b/w illustrations, 3 illustrations in colour
Topics: Numerical Analysis, Differential Geometry, Systems Theory, Control, Topological Groups, Lie Groups, Non-associative Rings and Algebras