Discrete Mechanics, Geometric Integration and Lie–Butcher Series (eBook)
X, 361 Seiten
Springer International Publishing (Verlag)
978-3-030-01397-4 (ISBN)
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 and combinatorial 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.
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).
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).
Preface.- A. Iserles and G.R.W. Quispel, Why geometric numerical integration?.- B. Owren, Lie group integrators.- H. Z. Munthe-Kaas and K. K. Føllesdal, Lie–Butcher series, Geometry, Algebra and Computation.- A. Murua and J. M. Sanz-Serna, Averaging and computing normal forms with word series algorithms.- L. A. Duffaut Espinosa, K. Ebrahimi-Fard, and W. Steven Gray, Combinatorial Hopf algebras for interconnected nonlinear input-output systems with a view towards discretization.- F. Casas, Computational aspects of some exponential identities.- K. Ebrahimi-Fard and I. Mencattini, Post-Lie Algebras, Factorization Theorems and Isospectral Flows.- G. Bogfjellmo, R. Dahmen, and A.Schmeding, Overview of (pro-)Lie group structures on Hopf algebra character groups,.- M. Barbero Liñán and D. Martín de Diego, Bäcklund transformations in discrete variational principles for Lie–Poisson equations.- M. Vermeeren, Numerical precession in variational discretizations of the Kepler problem.- O. Verdier, Full affine equivariance and weak natural transformations in numerical analysis - the case of B-Series.- References.
| Erscheint lt. Verlag | 5.11.2018 |
|---|---|
| Reihe/Serie | Springer Proceedings in Mathematics & Statistics | Springer Proceedings in Mathematics & Statistics |
| Zusatzinfo | X, 361 p. 169 illus., 3 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | 37C10, 70G65, 93B25, 17B99, 22E65, 65P10 • 65D30, 34A26, 15A16, 34C40, 16T05, 70G75 • Baker–Campbell–Hausdorff formula • Chen-Fliess series • Discrete Mechanics • Geometric Integration • Hopf Algebras • Lie–Butcher Series • Lie group integrators • Lie groups • Magnus expansion • Nonlinear Control Theory • word series |
| ISBN-10 | 3-030-01397-9 / 3030013979 |
| ISBN-13 | 978-3-030-01397-4 / 9783030013974 |
| Haben Sie eine Frage zum Produkt? |
PDF (Wasserzeichen)Größe: 4,9 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich
