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
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8
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8
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یادداشتهای مربوط به خلاصه یا چکیده
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.--
یادداشتهای مربوط به سفارشات
منبع سفارش / آدرس اشتراک
Springer Nature
شماره انبار
com.springer.onix.9783030013974
ویراست دیگر از اثر در قالب دیگر رسانه
عنوان
Discrete mechanics, geometric integration and Lie-Butcher series.
شماره استاندارد بين المللي کتاب و موسيقي
9783030013967
عنوان اصلی به زبان دیگر
عنوان اصلي به زبان ديگر
DMGILBS
موضوع (اسم عام یاعبارت اسمی عام)
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.
مقوله موضوعی
موضوع مستند نشده
MAT-- 002040
موضوع مستند نشده
PBKS
موضوع مستند نشده
PBKS
رده بندی ديویی
شماره
512/
.
482
ويراست
23
رده بندی کنگره
شماره رده
QA252
.
3
نام شخص - (مسئولیت معنوی برابر )
مستند نام اشخاص تاييد نشده
Barbero Liñán, María
مستند نام اشخاص تاييد نشده
Ebrahimi-Fard, Kurusch,1973-
نام تنالگان به منزله سر شناسه - (مسئولیت معنوی درجه اول )
مستند نام تنالگان تاييد نشده
International Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series(2015 :, Madrid, Spain)