Skip to main content
SpringerLink
Log in
Book cover

Discrete Mechanics, Geometric Integration and Lie–Butcher Series

DMGILBS, Madrid, May 2015

  • Conference proceedings
  • © 2018

Overview

Editors:
  1. Kurusch Ebrahimi-Fard

    1. Department of Mathematical Sciences, Norwegian University of Science and Technology—NTNU, Trondheim, Norway

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. María Barbero Liñán

    1. Institute for the Mathematical Sciences (ICMAT), Madrid, Spain

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • 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.

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (11 papers)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Why Geometric Numerical Integration?

    • Arieh Iserles, G. R. W. Quispel
    Pages 1-28

  3. Lie Group Integrators

    • Brynjulf Owren
    Pages 29-69

  4. Lie–Butcher Series, Geometry, Algebra and Computation

    • Hans Z. Munthe-Kaas, Kristoffer K. Føllesdal
    Pages 71-113

  5. Averaging and Computing Normal Forms with Word Series Algorithms

    • Ander Murua, Jesús M. Sanz-Serna
    Pages 115-137

  6. Combinatorial Hopf Algebras for Interconnected Nonlinear Input-Output Systems with a View Towards Discretization

    • Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
    Pages 139-183

  7. Computational Aspects of Some Exponential Identities

    • Fernando Casas
    Pages 185-229

  8. Post-Lie Algebras, Factorization Theorems and Isospectral Flows

    • Kurusch Ebrahimi-Fard, Igor Mencattini
    Pages 231-285

  9. Overview of (pro-)Lie Group Structures on Hopf Algebra Character Groups

    • Geir Bogfjellmo, Rafael Dahmen, Alexander Schmeding
    Pages 287-314

  10. Bäcklund Transformations in Discrete Variational Principles for Lie-Poisson Equations

    • María Barbero Liñán , David Martín de Diego
    Pages 315-332

  11. Numerical Precession in Variational Discretizations of the Kepler Problem

    • Mats Vermeeren
    Pages 333-348

  12. Full Affine Equivariance and Weak Natural Transformations in Numerical Analysis—The Case of B-Series

    • Olivier Verdier
    Pages 349-361
Back to top

Keywords

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. 



Editors and Affiliations

  • Department of Mathematical Sciences, Norwegian University of Science and Technology—NTNU, Trondheim, Norway

    Kurusch Ebrahimi-Fard

  • Institute for the Mathematical Sciences (ICMAT), Madrid, Spain

    María Barbero Liñán

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

Publish with us

Policies and ethics

Back to top

Search

Navigation