عنوان

Discrete mechanics, geometric integration and Lie-Butcher series :

شابک

3030013979

شابک

9783030013974

شابک اشتباه

3030013960

شابک اشتباه

9783030013967

عنوان اصلي

Discrete mechanics, geometric integration and Lie-Butcher series :

نام عام مواد

[Book]

ساير اطلاعات عنواني

DMGILBS, Madrid, May 2015 /

نام نخستين پديدآور

Kurusch Ebrahimi-Fard, María Barbero Liñán, editors.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource (x, 361 pages) :

ساير جزييات

illustrations (some color)

عنوان فروست

Springer proceedings in mathematics & statistics,

مشخصه جلد

volume 267

شاپا ي ISSN فروست

2194-1009 ;

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

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.--

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030013974

عنوان

Discrete mechanics, geometric integration and Lie-Butcher series.

شماره استاندارد بين المللي کتاب و موسيقي

9783030013967

عنوان اصلي به زبان ديگر

DMGILBS

موضوع مستند نشده

Lie algebras, Congresses.

موضوع مستند نشده

Lie groups, Congresses.

موضوع مستند نشده

Algebra.

موضوع مستند نشده

Cybernetics & systems theory.

موضوع مستند نشده

Differential & Riemannian geometry.

موضوع مستند نشده

Groups & group theory.

موضوع مستند نشده

Lie algebras.

موضوع مستند نشده

Lie groups.

موضوع مستند نشده

MATHEMATICS-- Algebra-- Intermediate.

موضوع مستند نشده

Numerical analysis.

موضوع مستند نشده

MAT-- 002040

موضوع مستند نشده

PBKS

موضوع مستند نشده

PBKS

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Barbero Liñán, María

مستند نام اشخاص تاييد نشده

Ebrahimi-Fard, Kurusch,1973-

مستند نام تنالگان تاييد نشده

International Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series(2015 :, Madrid, Spain)

تاريخ عمليات

20200823072936.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y