© 2018

Discrete Mechanics, Geometric Integration and Lie–Butcher Series

DMGILBS, Madrid, May 2015

  • Kurusch Ebrahimi-Fard
  • María Barbero Liñán


  • 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

Conference proceedings

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 267)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Arieh Iserles, G. R. W. Quispel
    Pages 1-28
  3. Brynjulf Owren
    Pages 29-69
  4. Hans Z. Munthe-Kaas, Kristoffer K. Føllesdal
    Pages 71-113
  5. Ander Murua, Jesús M. Sanz-Serna
    Pages 115-137
  6. Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
    Pages 139-183
  7. Kurusch Ebrahimi-Fard, Igor Mencattini
    Pages 231-285
  8. Geir Bogfjellmo, Rafael Dahmen, Alexander Schmeding
    Pages 287-314
  9. María Barbero Liñán , David Martín de Diego
    Pages 315-332

About these proceedings


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. 


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

Editors and affiliations

  • Kurusch Ebrahimi-Fard
    • 1
  • María Barbero Liñán
    • 2
  1. 1.Department of Mathematical SciencesNorwegian University of Science and Technology—NTNUTrondheimNorway
  2. 2.Institute for the Mathematical Sciences (ICMAT)MadridSpain

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