Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Hairer, E.
Автор: Hairer Ernst, Lubich Christian, Wanner Gerhard Название: Geometric Numerical Integration / Structure-Preserving Algorithms for Ordinary Differential Equations ISBN: 3540430032 ISBN-13(EAN): 9783540430032 Издательство: Springer Цена: 7943 р. Наличие на складе: Поставка под заказ. Описание: Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
Описание: Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
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.
Описание: This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.
Описание: A text for a graduate level course in the theory of ordinary differential equations. It contains theory and applications. It links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and abstract algebra.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru