|
" Discrete mechanics, geometric integration and Lie-Butcher series : "
Kurusch Ebrahimi-Fard, María Barbero Liñán, editors.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
859469
|
| Main Entry
|
:
|
International Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series(2015 :, Madrid, Spain)
|
| Title & Author
|
:
|
Discrete mechanics, geometric integration and Lie-Butcher series : : DMGILBS, Madrid, May 2015 /\ Kurusch Ebrahimi-Fard, María Barbero Liñán, editors.
|
| Publication Statement
|
:
|
Cham, Switzerland :: Springer,, 2018.
|
| Series Statement
|
:
|
Springer proceedings in mathematics & statistics,; volume 267
|
| Page. NO
|
:
|
1 online resource (x, 361 pages) :: illustrations (some color)
|
| ISBN
|
:
|
3030013979
|
|
|
:
|
: 9783030013974
|
|
|
:
|
3030013960
|
|
|
:
|
9783030013967
|
| Contents
|
:
|
Intro; Preface; Contents; Contributors; Why Geometric Numerical Integration?; 1 The Purpose of GNI; 2 The Story So Far; 2.1 Symplectic Integration; 2.2 Lie-Group Methods; 2.3 Conservation of Volume; 2.4 Preserving Energy and Other First Integrals; 3 Four Recent Stories of GNI; 3.1 Highly Oscillatory Hamiltonian Systems; 3.2 Kahan's `Unconventional' Method; 3.3 Applications to Celestial Mechanics; 3.4 Symmetric Zassenhaus Splitting and the Equations of Quantum Mechanics; 4 Beyond GNI; 4.1 GNI Meets Abstract Algebra; 4.2 Highly Oscillatory Quadrature; 4.3 Structured Linear Algebra; References
|
|
|
:
|
3 Averaging of Quasiperiodically Forced Systems3.1 The Solution of the Oscillatory Problem; 3.2 The Transport Equation; 3.3 The Averaged System and the Change of Variables; 3.4 Geometric Properties; 3.5 Finding the Coefficients; 3.6 Changing the Initial Time; 4 Autonomous Problems; 4.1 Perturbed Problems; 4.2 The Transport Equation. Normal Forms; 5 Further Extensions; 5.1 Extended Word Series; 5.2 More General Perturbed Problems; References; Combinatorial Hopf Algebras for Interconnected Nonlinear Input-Output Systems with a View Towards Discretization; 1 Introduction; 2 Preliminaries
|
|
|
:
|
4.2 Operations on Forests Computed by Recursions in a Magma4.3 Combinatorial Functions on Ordered Forests; 4.4 Concatenation and De-concatenation; 4.5 Shuffle and De-shuffle; 4.6 Grafting, Pruning, GL Product and GL Coproduct; 4.7 Substitution, Co-substitution, Scaling and Derivation; 4.8 Exponentials and Logarithms; 5 Concluding Remarks; 5.1 Programming in Haskell; References; Averaging and Computing Normal Forms with Word Series Algorithms; 1 Introduction; 2 Word Series; 2.1 Defining Word Series; 2.2 The Convolution Product; 2.3 Universal Formulations
|
|
|
:
|
6.2 Selecting a Minimal Set of Conditions7 Symplectic Lie Group Integrators; 7.1 Variational Integrators on Lie Groups; 8 Preservation of First Integrals; References; Lie-Butcher Series, Geometry, Algebra and Computation; 1 Introduction; 2 Geometry of Lie-Butcher Series; 2.1 Parallel Transport; 2.2 The Flat Cartan Connection on a Lie Group; 2.3 Numerical Integration; 3 Algebraic Structures of Lie-Butcher Theory; 3.1 Algebras; 3.2 Morphisms and Free Objects; 3.3 Enveloping Algebras; 4 Computing with Lie-Butcher Series; 4.1 Operations on Infinite Series Computed by Dualisation
|
|
|
:
|
Lie Group Integrators1 Introduction; 2 The Setup; 3 Types of Schemes; 3.1 Schemes of Munthe-Kaas Type; 3.2 Integrators Based on Compositions of Flows; 4 Choice of Lie Group Actions; 4.1 Lie Group Acting on Itself by Multiplication; 4.2 The Affine Group and Its Use in Semilinear PDE Methods; 4.3 The Coadjoint Action and Lie-Poisson Systems; 4.4 Homogeneous Spaces and the Stiefel and Grassmann Manifolds; 4.5 Isospectral Flows; 4.6 Tangent and Cotangent Bundles; 5 Isotropy; 6 Order Theory for Lie Group Integrators; 6.1 Order Conditions for Commutator-Free Lie Group Integrators
|
| Abstract
|
:
|
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.--
|
| Subject
|
:
|
Lie algebras, Congresses.
|
| Subject
|
:
|
Lie groups, Congresses.
|
| Subject
|
:
|
Algebra.
|
| Subject
|
:
|
Cybernetics systems theory.
|
| Subject
|
:
|
Differential Riemannian geometry.
|
| Subject
|
:
|
Groups group theory.
|
| Subject
|
:
|
Lie algebras.
|
| Subject
|
:
|
Lie groups.
|
| Subject
|
:
|
MATHEMATICS-- Algebra-- Intermediate.
|
| Subject
|
:
|
Numerical analysis.
|
| Dewey Classification
|
:
|
512/.482
|
| LC Classification
|
:
|
QA252.3
|
| Added Entry
|
:
|
Barbero Liñán, María
|
|
|
:
|
Ebrahimi-Fard, Kurusch,1973-
|
| Parallel Title
|
:
|
DMGILBS
|
| |