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# Dynamical Systems Method For Solving Operator Equations

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**📒Dynamical Systems Method For Solving Nonlinear Operator Equations ✍ Alexander G. Ramm**

**Dynamical Systems Method for Solving Nonlinear Operator Equations**

✏Author :

**Alexander G. Ramm**

✏Publisher :

**Elsevier**

✏Release Date :

**2006-09-25**

✏Pages :

**304**

✏ISBN :

**0080465560**

✏Available Language :

**English, Spanish, And French**

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**✏Dynamical Systems Method for Solving Nonlinear Operator Equations Book Summary :** 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)

**📒Dynamical Systems Method And Applications ✍ Alexander G. Ramm**

**Dynamical Systems Method and Applications**

✏Author :

**Alexander G. Ramm**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2013-06-07**

✏Pages :

**576**

✏ISBN :

**9781118199602**

✏Available Language :

**English, Spanish, And French**

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**✏Dynamical Systems Method and Applications Book Summary :** 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.

**📒Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems ✍ Krzysztof Kowalski**

**Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems**

✏Author :

**Krzysztof Kowalski**

✏Publisher :

**World Scientific**

✏Release Date :

**1994**

✏Pages :

**122**

✏ISBN :

**9810217536**

✏Available Language :

**English, Spanish, And French**

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**✏Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems Book Summary :** 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 Schrdinger-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, Bcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

**Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology**

✏Author :

✏Publisher :

✏Release Date :

✏Pages :

✏ISBN :

**9789814479264**

✏Available Language :

**English, Spanish, And French**

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**✏Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology Book Summary :**

**📒Information Computing And Applications ✍ Chunfeng Liu**

**Information Computing and Applications**

✏Author :

**Chunfeng Liu**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2011-12-05**

✏Pages :

**716**

✏ISBN :

**9783642275029**

✏Available Language :

**English, Spanish, And French**

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**✏Information Computing and Applications Book Summary :** 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.

**Numerical Time Dependent Partial Differential Equations for Scientists and Engineers**

✏Author :

**Moysey Brio**

✏Publisher :

**Academic Press**

✏Release Date :

**2010-09-21**

✏Pages :

**312**

✏ISBN :

**0080917046**

✏Available Language :

**English, Spanish, And French**

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**✏Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book Summary :** 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 ✍ Herold G. Dehling**

**Stochastic Modelling in Process Technology**

✏Author :

**Herold G. Dehling**

✏Publisher :

**Elsevier**

✏Release Date :

**2007-07-03**

✏Pages :

**290**

✏ISBN :

**0080548970**

✏Available Language :

**English, Spanish, And French**

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**✏Stochastic Modelling in Process Technology Book Summary :** 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

**Annales Polonici Mathematici**

✏Author :

✏Publisher :

✏Release Date :

**2009**

✏Pages :

✏ISBN :

**UOM:39015085193749**

✏Available Language :

**English, Spanish, And French**

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**✏Annales Polonici Mathematici Book Summary :**

**📒Nonlinear Dynamical Systems In Engineering ✍ Vasile Marinca**

**Nonlinear Dynamical Systems in Engineering**

✏Author :

**Vasile Marinca**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2012-01-05**

✏Pages :

**396**

✏ISBN :

**9783642227356**

✏Available Language :

**English, Spanish, And French**

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**✏Nonlinear Dynamical Systems in Engineering Book Summary :** 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.

**Numerical Mathematics**

✏Author :

✏Publisher :

✏Release Date :

**2007**

✏Pages :

✏ISBN :

**UOM:39015072605630**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Mathematics Book Summary :**

**📒Nonclassical Linear Volterra Equations Of The First Kind ✍ Anatoly S. Apartsyn**

**Nonclassical Linear Volterra Equations of the First Kind**

✏Author :

**Anatoly S. Apartsyn**

✏Publisher :

**Walter de Gruyter**

✏Release Date :

**2003-01-01**

✏Pages :

**174**

✏ISBN :

**9783110944976**

✏Available Language :

**English, Spanish, And French**

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**✏Nonclassical Linear Volterra Equations of the First Kind Book Summary :** 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.

**📒Dynamic Impulse Systems ✍ S.T. Zavalishchin**

**Dynamic Impulse Systems**

✏Author :

**S.T. Zavalishchin**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2013-03-14**

✏Pages :

**260**

✏ISBN :

**9789401588935**

✏Available Language :

**English, Spanish, And French**

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**✏Dynamic Impulse Systems Book Summary :** A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco momics and biology, have an irregular structure: classical variational proce dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.

**📒Approximate Solution Of Operator Equations With Applications ✍ Ioannis K. Argyros**

**Approximate Solution of Operator Equations with Applications**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**World Scientific**

✏Release Date :

**2005**

✏Pages :

**512**

✏ISBN :

**9789812563651**

✏Available Language :

**English, Spanish, And French**

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**✏Approximate Solution of Operator Equations with Applications Book Summary :** 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.

**📒Algebraic And Symbolic Computation Methods In Dynamical Systems ✍ Alban Quadrat**

**Algebraic and Symbolic Computation Methods in Dynamical Systems**

✏Author :

**Alban Quadrat**

✏Publisher :

**Springer Nature**

✏Release Date :

**2020-05-30**

✏Pages :

**311**

✏ISBN :

**9783030383565**

✏Available Language :

**English, Spanish, And French**

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**✏Algebraic and Symbolic Computation Methods in Dynamical Systems Book Summary :** This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

**📒Differential Equations Dynamical Systems And Linear Algebra ✍ Morris W. Hirsch**

**Differential Equations Dynamical Systems and Linear Algebra**

✏Author :

**Morris W. Hirsch**

✏Publisher :

**Academic Press**

✏Release Date :

**1974-06-28**

✏Pages :

**358**

✏ISBN :

**9780080873763**

✏Available Language :

**English, Spanish, And French**

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**✏Differential Equations Dynamical Systems and Linear Algebra Book Summary :** This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

**Mathematical Reviews**

✏Author :

✏Publisher :

✏Release Date :

**2007**

✏Pages :

✏ISBN :

**UOM:39015078588616**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Mathematical Reviews Book Summary :**

**📒Linear Time Varying Approximations To Nonlinear Dynamical Systems ✍ Maria Tomas-Rodriguez**

**Linear Time varying Approximations to Nonlinear Dynamical Systems**

✏Author :

**Maria Tomas-Rodriguez**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2010-02-04**

✏Pages :

**300**

✏ISBN :

**9781849961004**

✏Available Language :

**English, Spanish, And French**

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**✏Linear Time varying Approximations to Nonlinear Dynamical Systems Book Summary :** Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

**📒Semigroups Of Operators Theory And Applications ✍ A.V. Balakrishnan**

**Semigroups of Operators Theory and Applications**

✏Author :

**A.V. Balakrishnan**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2000-08-01**

✏Pages :

**367**

✏ISBN :

**376436310X**

✏Available Language :

**English, Spanish, And French**

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**✏Semigroups of Operators Theory and Applications Book Summary :** 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 ✍ Robert A. Meyers**

**Mathematics of Complexity and Dynamical Systems**

✏Author :

**Robert A. Meyers**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2011-10-05**

✏Pages :

**1858**

✏ISBN :

**9781461418054**

✏Available Language :

**English, Spanish, And French**

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**✏Mathematics of Complexity and Dynamical Systems Book Summary :** 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 ✍ Ioannis K. Argyros**

**Numerical Methods for Equations and its Applications**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**CRC Press**

✏Release Date :

**2012-06-05**

✏Pages :

**474**

✏ISBN :

**9781466517110**

✏Available Language :

**English, Spanish, And French**

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**✏Numerical Methods for Equations and its Applications Book Summary :** 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 ✍ Alexander G. Ramm**

**Random Fields Estimation**

✏Author :

**Alexander G. Ramm**

✏Publisher :

**World Scientific**

✏Release Date :

**2005**

✏Pages :

**373**

✏ISBN :

**9789812565365**

✏Available Language :

**English, Spanish, And French**

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**✏Random Fields Estimation Book Summary :** 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 ✍ Valery I. Klyatskin**

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

✏Author :

**Valery I. Klyatskin**

✏Publisher :

**Springer**

✏Release Date :

**2014-07-14**

✏Pages :

**418**

✏ISBN :

**9783319075877**

✏Available Language :

**English, Spanish, And French**

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**✏Stochastic Equations Theory and Applications in Acoustics Hydrodynamics Magnetohydrodynamics and Radiophysics Volume 1 Book Summary :** 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.

**📒Averaging Methods In Nonlinear Dynamical Systems ✍ Jan A. Sanders**

**Averaging Methods in Nonlinear Dynamical Systems**

✏Author :

**Jan A. Sanders**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2007-08-18**

✏Pages :

**434**

✏ISBN :

**9780387489186**

✏Available Language :

**English, Spanish, And French**

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**✏Averaging Methods in Nonlinear Dynamical Systems Book Summary :** Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.

**📒Efficient Approximation Methods For The Global Long Term Behavior Of Dynamical Systems ✍ Péter Koltai**

**Efficient Approximation Methods for the Global Long term Behavior of Dynamical Systems**

✏Author :

**Péter Koltai**

✏Publisher :

**Logos Verlag Berlin GmbH**

✏Release Date :

**2011**

✏Pages :

**162**

✏ISBN :

**9783832527525**

✏Available Language :

**English, Spanish, And French**

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**✏Efficient Approximation Methods for the Global Long term Behavior of Dynamical Systems Book Summary :** Fur die Analyse des Langzeitverhaltens dynamischer Systeme werden in dieser Dissertation drei neue Ansatze, basierend auf Transferoperator-Methoden, zur Entwicklung effizienter Algorithmen vorgestellt. Zuerst leiten wir eine Diskretisierung auf dunnen Gittern her, um den Fluch der Dimension in den Griff zu bekommen. Die zweite Methode behandelt den infinitesimalen Generator der Transferoperator-Halbgruppe fur zeit-kontinuierliche Systeme. Als Drittes benutzen wir mean-field-Theorie, um die Dynamik von Subsystemen zu beschreiben, wobei besonderes Augenmerk auf die Konformationsanalyse in der Molekuldynamik gerichtet wird. Des Weiteren werden Bedingungen hergeleitet, unter welchen die Galerkin-Projektion des Transferoperators mit einer kleinen zufalligen Storung des zugrunde liegenden Systems in Verbindung gebracht werden kann. In this thesis three new transfer operator based approaches are developed for the analysis of the long-term behavior of dynamical systems. First, a sparse grid discretization is derived in order to deal with the "curse of dimension". The second method considers the infinitesimal generator of the transfer operator semigroup for continuous-time systems. The third method uses mean field theory to describe the dynamics of subsystems; here the main attention is devoted to conformation analysis in molecular dynamics. Further, conditions are derived such that the Galerkin projection of the transfer operator can be related to a small random perturbation of the underlying system.

**📒Orthogonal Sets And Polar Methods In Linear Algebra ✍ Enrique Castillo**

**Orthogonal Sets and Polar Methods in Linear Algebra**

✏Author :

**Enrique Castillo**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2011-10-14**

✏Pages :

**422**

✏ISBN :

**9781118031148**

✏Available Language :

**English, Spanish, And French**

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**✏Orthogonal Sets and Polar Methods in Linear Algebra Book Summary :** A unique, applied approach to problem solving in linearalgebra Departing from the standard methods of analysis, this unique bookpresents methodologies and algorithms based on the concept oforthogonality and demonstrates their application to both standardand novel problems in linear algebra. Covering basic theory oflinear systems, linear inequalities, and linear programming, itfocuses on elegant, computationally simple solutions to real-worldphysical, economic, and engineering problems. The authors clearlyexplain the reasons behind the analysis of different structures andconcepts and use numerous illustrative examples to correlate themathematical models to the reality they represent. Readers aregiven precise guidelines for: * Checking the equivalence of two systems * Solving a system in certain selected variables * Modifying systems of equations * Solving linear systems of inequalities * Using the new exterior point method * Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables,end-of-chapter exercises as well as Java and Mathematica programsavailable from the authors' Web site, this is an invaluabletext/reference for mathematicians, engineers, applied scientists,and graduate students in mathematics.

**📒Numerical Solution Of Ordinary Differential Equations ✍ Kendall Atkinson**

**Numerical Solution of Ordinary Differential Equations**

✏Author :

**Kendall Atkinson**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2011-10-24**

✏Pages :

**272**

✏ISBN :

**9781118164525**

✏Available Language :

**English, Spanish, And French**

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**✏Numerical Solution of Ordinary Differential Equations Book Summary :** A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

**📒Nonlinear Evolution Equations And Dynamical Systems ✍ V. G. Makhanʹkov**

**Nonlinear Evolution Equations and Dynamical Systems**

✏Author :

**V. G. Makhanʹkov**

✏Publisher :

**Springer Verlag**

✏Release Date :

**1991**

✏Pages :

**240**

✏ISBN :

**UOM:39015049316154**

✏Available Language :

**English, Spanish, And French**

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**✏Nonlinear Evolution Equations and Dynamical Systems Book Summary :**

**📒Efficient Methods For Solving Equations And Variational Inequalities ✍ Ioannis Konstantinos Argyros**

**Efficient Methods for Solving Equations and Variational Inequalities**

✏Author :

**Ioannis Konstantinos Argyros**

✏Publisher :

**Polimetrica s.a.s.**

✏Release Date :

**2009**

✏Pages :

**603**

✏ISBN :

**9788876991493**

✏Available Language :

**English, Spanish, And French**

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**✏Efficient Methods for Solving Equations and Variational Inequalities Book Summary :**

**📒Solutions Manual To Accompany Beginning Partial Differential Equations ✍ Peter V. O'Neil**

**Solutions Manual to Accompany Beginning Partial Differential Equations**

✏Author :

**Peter V. O'Neil**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2014-10-13**

✏Pages :

**128**

✏ISBN :

**9781118630099**

✏Available Language :

**English, Spanish, And French**

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**✏Solutions Manual to Accompany Beginning Partial Differential Equations Book Summary :** Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy.

**📒Nonlinear Dynamical Systems And Control ✍ Wassim M. Haddad**

**Nonlinear Dynamical Systems and Control**

✏Author :

**Wassim M. Haddad**

✏Publisher :

**Princeton University Press**

✏Release Date :

**2011-09-19**

✏Pages :

**944**

✏ISBN :

**9781400841042**

✏Available Language :

**English, Spanish, And French**

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**✏Nonlinear Dynamical Systems and Control Book Summary :** Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.