Dynamical Systems Method For Solving Nonlinear Operator Equations
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Dynamical Systems Method For Solving Nonlinear Operator Equations
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Author : Alexander G. Ramm
language : en
Publisher: Elsevier
Release Date : 2006-09-25
Dynamical Systems Method For Solving Nonlinear Operator Equations written by Alexander G. Ramm and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-25 with Mathematics categories.
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
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Author : Alexander G. Ramm
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-07
Dynamical Systems Method And Applications written by Alexander G. Ramm and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Mathematics categories.
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.
Nonlinear Differential Equations And Dynamical Systems
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Author : Feliz Manuel Minhós
language : en
Publisher: MDPI
Release Date : 2021-04-15
Nonlinear Differential Equations And Dynamical Systems written by Feliz Manuel Minhós and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Nonlinear Differential Equations And Dynamical Systems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Differential Equations And Dynamical Systems written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems
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Author : Krzysztof Kowalski
language : en
Publisher: World Scientific
Release Date : 1994
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems written by Krzysztof Kowalski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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
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Author : Santiago Cano-casanova
language : en
Publisher: World Scientific
Release Date : 2005-09-29
Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology written by Santiago Cano-casanova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-29 with Science categories.
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology.The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis — from the most abstract developments up to the most concrete applications to population dynamics and socio-biology — in an effort to fill the existing gaps between these fields.
Integral Equations Boundary Value Problems And Related Problems
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Author : Xing Li
language : en
Publisher: World Scientific
Release Date : 2013-03-07
Integral Equations Boundary Value Problems And Related Problems written by Xing Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.
In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.
Averaging Methods In Nonlinear Dynamical Systems
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Author : Jan A. Sanders
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-18
Averaging Methods In Nonlinear Dynamical Systems written by Jan A. Sanders and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-18 with Mathematics categories.
Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice 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 profuse, illuminating diagrams." - Mathematical Reviews
Computational Methods In Nonlinear Analysis
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Author : Ioannis K. Argyros
language : en
Publisher: World Scientific
Release Date : 2013
Computational Methods In Nonlinear Analysis written by Ioannis K. Argyros and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.
Nonlinear Systems And Matrix Analysis Recent Advances In Theory And Applications
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Author : Peter Chen
language : en
Publisher: BoD – Books on Demand
Release Date : 2024-11-27
Nonlinear Systems And Matrix Analysis Recent Advances In Theory And Applications written by Peter Chen and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-27 with Mathematics categories.
Nonlinear system analysis is of interest to engineers, sociologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. In mathematics, a nonlinear system does not satisfy the superposition principle such as in a linear system. Therefore, the theories underlining nonlinear analysis and their applications need to be developed on their own merit. The first section of this book is a collection of examples reporting recent advances in both theory and applications of nonlinear system analysis. The contents of each chapter will provide in-depth foresight to interested readers. As numerical linearization to a set of matrix equations is still the principal method used to solve a nonlinear system, matrix analysis is the topic of the second section of this book. The matrices have invaded practically all areas of mathematics, the experimental and social sciences, engineering, and technology. This volume updates purely mathematical theoretical aspects, and it also presents concrete examples of the wide range of applications of matrix theory in other disciplines.