Geometric Numerical Integration / Structure-Preserving Algorithms for Ordinary Differential Equations, Hairer Ernst, Lubich Christian, Wanner Gerhard
Автор: Hairer, E. Название: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations ISBN: 3540306633 ISBN-13(EAN): 9783540306634 Издательство: Springer Цена: 14959 р. Наличие на складе: Есть у поставщикаПоставка под заказ. Описание: Provides information on numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. This book presents a theory of symplectic and symmetric methods, including composition, splitting, multistep and various specially designed integrators.
Автор: Hairer Название: Geometric numerical integration ISBN: 364205157X ISBN-13(EAN): 9783642051579 Издательство: Springer Цена: 9349 р. Наличие на складе: Есть у поставщикаПоставка под заказ. Описание: This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions.
Описание: Provides information on numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. This book presents a theory of symplectic and symmetric methods, including composition, splitting, multistep and various specially designed integrators.
Описание: The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He introduces the variational formulation of boundary value problems together with the necessary background from functional analysis and describes the finite element method including the most important error estimates. A more advanced chapter leads the reader into the theory of regularity. The reader will also find more details about the discretisation of singularly perturbed equations and eigenvalue problems. The author discusses the Stokes problem as an example of a saddle point problem taking into account its relevance to applications in fluid dynamics.
Описание: The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment, so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through discretization methods, algorithms, software design, verification, and computational examples.
Описание: This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Описание: Includes the proof of the fundamental Doob-Meyer decomposition theorem. This book contains the more general version of the Girsanov theorem due to Lenglart and martingale representation, including both the Jacod-Yor theory and Emery`s examples of martingales that actually have martingale representation.
Описание: This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises.
Описание: This book contains a modern introduction to the use of finite difference and finite element methods for the computer solution of ordinary and partial differential equations. After a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved, the balance of the content introduces, analyzes and implements, using FORTRAN90 and MATLAB programs, the more commonly used finite difference and finite element methods for solving a variety of problems, including both initial value and boundary value problems.
Описание: Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB(R) teaches you how to numerically solve both ordinary and partial differential equations with ease. This innovative resource brings together a skillful treatment of MATLAB and programming alongside current theory and modeling methods. All the tools needed to master MATLAB and then use it to solve differential equations are provided. "Exercises for the Reader" range from routine computations to more advanced conceptual and theoretical questions, while illustrative examples demonstrate MATLAB's powerful ability to solve differential equations. With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB(R) is an unsurpassed pedagogical tool.
Описание: Second edition of the exceptionally popular Numerical Analysis of Ordinary Differential Equations New exercises are included in each chapter The author is widely regarded as the world expert on Runge-Kutta methods "This book is...an indispensible reference for any researcher" - American Mathematical Society review of the first edition.
Описание: Written for undergraduate students with a mathematical background, this book is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. It features numerous theoretical and computational examples.
Описание: In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author`s pioneering text is fully revised and updated to acknowledge many of these developments.
Автор: Atkinson, Kendall E. Han, Weimin Stewart, David E. Название: Numerical solution of ordinary differential equations ISBN: 047004294X ISBN-13(EAN): 9780470042946 Издательство: Wiley Рейтинг: Цена: 10084 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers an introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). This book contains many references to both analytical and numerical ODE literature while presenting unifying views on different problem classes. It is suitable for students in mathematics, engineering, and the sciences.
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