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Dynamical Systems Method For Solving Operator Equations

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Dynamical Systems Method and Applications

Dynamical Systems Method and Applications Book
Author : Alexander G. Ramm,Nguyen S. Hoang
Publisher : John Wiley & Sons
Release : 2013-06-07
ISBN : 111819960X
Language : En, Es, Fr & De

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Book Description :

Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

Dynamical Systems Method for Solving Nonlinear Operator Equations

Dynamical Systems Method for Solving Nonlinear Operator Equations Book
Author : Alexander G. Ramm
Publisher : Elsevier
Release : 2006-09-25
ISBN : 9780080465562
Language : En, Es, Fr & De

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Book Description :

Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author. Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed Self-contained, suitable for wide audience Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes)

Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology

Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology Book
Author : Anonim
Publisher : Unknown
Release : 2020-12-05
ISBN : 9814479268
Language : En, Es, Fr & De

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Book Description :

Download Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Information Computing and Applications

Information Computing and Applications Book
Author : Chunfeng Liu,Jincai Chang,Aimin Yang
Publisher : Springer Science & Business Media
Release : 2011-12-05
ISBN : 3642275028
Language : En, Es, Fr & De

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Book Description :

The two-volume set, CCIS 243 and CCIS 244, constitutes the refereed proceedings of the Second International Conference on Information Computing and Applications, ICICA 2010, held in Qinhuangdao, China, in October 2011. The 191 papers presented in both volumes were carefully reviewed and selected from numerous submissions. They are organized in topical sections on computational statistics, social networking and computing, evolutionary computing and applications, information education and application, internet and web computing, scientific and engineering computing, system simulation computing, bio-inspired and DNA computing, internet and Web computing, multimedia networking and computing, parallel and distributed computing.

Annales Polonici Mathematici

Annales Polonici Mathematici Book
Author : Anonim
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Annales Polonici Mathematici book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book
Author : Moysey Brio,Gary M. Webb,Aramais R. Zakharian
Publisher : Academic Press
Release : 2010-09-21
ISBN : 9780080917047
Language : En, Es, Fr & De

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Book Description :

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

Stochastic Modelling in Process Technology

Stochastic Modelling in Process Technology Book
Author : Herold G. Dehling,Timo Gottschalk,Alex C. Hoffmann
Publisher : Elsevier
Release : 2007-07-03
ISBN : 9780080548975
Language : En, Es, Fr & De

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Book Description :

There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. Introduction to stochastic process modelling as an alternative modelling technique Shows how stochastic modelling may be succesful where the traditional technique fails Overview of stochastic modelling in process technology in the research literature Illustration of the principle by a wide range of practical examples In-depth and self-contained discussions Points the way to both mathematical and technological research in a new, rewarding field

Numerical Mathematics

Numerical Mathematics Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Numerical Mathematics book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Nonlinear Dynamical Systems in Engineering

Nonlinear Dynamical Systems in Engineering Book
Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer Science & Business Media
Release : 2012-01-05
ISBN : 3642227341
Language : En, Es, Fr & De

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Book Description :

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Nonclassical Linear Volterra Equations of the First Kind

Nonclassical Linear Volterra Equations of the First Kind Book
Author : Anatoly S. Apartsyn
Publisher : Walter de Gruyter
Release : 2003-01-01
ISBN : 3110944979
Language : En, Es, Fr & De

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Book Description :

This monograph deals with linear integra Volterra equations of the first kind with variable upper and lower limits of integration. Volterra operators of this type are the basic operators for integral models of dynamic systems.

Approximate Solution of Operator Equations with Applications

Approximate Solution of Operator Equations with Applications Book
Author : Ioannis K. Argyros
Publisher : World Scientific
Release : 2005
ISBN : 9812563652
Language : En, Es, Fr & De

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Book Description :

Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.

Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems

Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems Book
Author : Krzysztof Kowalski
Publisher : World Scientific
Release : 1994
ISBN : 9789810217532
Language : En, Es, Fr & De

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Book Description :

This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schr”dinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, B„cklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Semigroups of Operators Theory and Applications

Semigroups of Operators  Theory and Applications Book
Author : A.V. Balakrishnan
Publisher : Springer Science & Business Media
Release : 2000-08-01
ISBN : 9783764363109
Language : En, Es, Fr & De

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Book Description :

These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems Book
Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Release : 2011-10-05
ISBN : 1461418054
Language : En, Es, Fr & De

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Book Description :

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Numerical Methods for Equations and its Applications

Numerical Methods for Equations and its Applications Book
Author : Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout
Publisher : CRC Press
Release : 2012-06-05
ISBN : 1466517115
Language : En, Es, Fr & De

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Book Description :

This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter co

Random Fields Estimation

Random Fields Estimation Book
Author : Alexander G. Ramm
Publisher : World Scientific
Release : 2005
ISBN : 9812565361
Language : En, Es, Fr & De

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Book Description :

This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.

Stochastic Equations Theory and Applications in Acoustics Hydrodynamics Magnetohydrodynamics and Radiophysics Volume 1

Stochastic Equations  Theory and Applications in Acoustics  Hydrodynamics  Magnetohydrodynamics  and Radiophysics  Volume 1 Book
Author : Valery I. Klyatskin
Publisher : Springer
Release : 2014-07-14
ISBN : 331907587X
Language : En, Es, Fr & De

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Book Description :

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Efficient Methods for Solving Equations and Variational Inequalities

Efficient Methods for Solving Equations and Variational Inequalities Book
Author : Ioannis Konstantinos Argyros,Saïd Hilout
Publisher : Polimetrica s.a.s.
Release : 2009
ISBN : 8876991492
Language : En, Es, Fr & De

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Book Description :

Download Efficient Methods for Solving Equations and Variational Inequalities book written by Ioannis Konstantinos Argyros,Saïd Hilout, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Nonlinear Evolution Equations and Dynamical Systems

Nonlinear Evolution Equations and Dynamical Systems Book
Author : V. G. Makhanʹkov,O. K. Pashaev
Publisher : Springer Verlag
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Nonlinear Evolution Equations and Dynamical Systems book written by V. G. Makhanʹkov,O. K. Pashaev, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.