Applications of Lie Groups to Difference Equations, Dorodnitsyn, Vladimir
Автор: Ronald E Mickens Название: Nonstandard Finite Difference Schemes: Methodology And Applications ISBN: 9811222533 ISBN-13(EAN): 9789811222535 Издательство: World Scientific Publishing Рейтинг: Цена: 17424.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
"This book contains a clear presentation of nonstandard finite difference schemes for the numerical integration of differential equations. A set of rules for constructing nonstandard finite difference schemes is also presented. An important feature of the book is the illustration of the various discrete modeling principles, by their application to a large number of both ordinary and partial differential equations."
Mathematical Reviews
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.
Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the "principle of dynamic consistency" and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Автор: R. M. M. Mattheij Название: Partial Differential Equations ISBN: 0898715946 ISBN-13(EAN): 9780898715941 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 21318.00 р. Наличие на складе: Нет в наличии.
Описание: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Автор: Hall Brian Название: Lie Groups, Lie Algebras, and Representations ISBN: 3319134663 ISBN-13(EAN): 9783319134666 Издательство: Springer Рейтинг: Цена: 7622.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.
In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:
a treatment of the Baker-Campbell-Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras
motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)
an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras
a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments
The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincar -Birkhoff-Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.
Review of the first edition
This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.
-- The Mathematical Gazette
Автор: Sergey Lemeshevsky, Piotr Matus, Dmitriy Poliakov Название: Exact Finite-Difference Schemes ISBN: 3110489643 ISBN-13(EAN): 9783110489644 Издательство: Walter de Gruyter Рейтинг: Цена: 18586.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations.
Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Описание: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. Exercises and student projects are available on the book’s webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.
Автор: Decio Levi; Rapha?l Rebelo; Pavel Winternitz Название: Symmetries and Integrability of Difference Equations ISBN: 3319566652 ISBN-13(EAN): 9783319566658 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.
Автор: Saber Elaydi; Yoshihiro Hamaya; Hideaki Matsunaga; Название: Advances in Difference Equations and Discrete Dynamical Systems ISBN: 9811064083 ISBN-13(EAN): 9789811064081 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016.
Автор: Ravi P. Agarwal; Claudio Cuevas; Carlos Lizama Название: Regularity of Difference Equations on Banach Spaces ISBN: 3319064460 ISBN-13(EAN): 9783319064468 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work introduces readers to the topic of maximal regularity for difference equations. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
Papers by Invited Speakers: Competitive exclusion through discrete time models: Azmy S. Ackleh and Paul L. Salceanu.- Benford solutions of linear difference equations: Arno Berger and Gideon Eshun.- Harvesting and dynamics in some one-dimensional population models: Eduardo Liz and Frank M. Hilker.- Chaos and wild chaos in Lorenz-type systems: Hinke M. Osinga, Bernd Krauskopf and Stefanie Hittmeyer.- Contributed Papers: Almost automorphic sequences and their application to a model of cellular neural network: Syed Abbas.- Advances in periodic difference equations with open problems: Ziyad AlSharawi, Jose S. Canovas and Antonio Linero.- An Evolutionary Beverton-Holt Model: J. M. Cushing.- The periodic decomposition problem: Balint Farkas and Szilard Gy. Revesz.- Existence of periodic and almost periodic solutions of discrete Ricker delay models: Yoshihiro Hamaya.- Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh Theory: Roman Simon Hilscher and Petr Zemanek.- Dynamic selection systems and replicator equations: Zdenek Pospsil.- Asymptotic equivalence of difference equations in Banach Space: Andrejs Reinfelds.
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Автор: Paul Cull; Mary Flahive; Robby Robson Название: Difference Equations ISBN: 1489988238 ISBN-13(EAN): 9781489988232 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers.
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron--Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly.
The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics.
Автор: Sigrun Bodine; Donald A. Lutz Название: Asymptotic Integration of Differential and Difference Equations ISBN: 3319182471 ISBN-13(EAN): 9783319182476 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the theory of asymptotic integration for both linear differential and difference equations.
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