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Dynamical Systems Method for Solving Nonlinear Operator Equations

2006-09-25 Mathematics
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Release : 2006-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 560/5 ( reviews)

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Book Synopsis Dynamical Systems Method for Solving Nonlinear Operator Equations by : Alexander G. Ramm

Download or read book Dynamical Systems Method for Solving Nonlinear Operator Equations written by Alexander G. Ramm. This book was released on 2006-09-25. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013-06-07 Mathematics
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Release : 2013-06-07
Genre : Mathematics
Kind : eBook
Book Rating : 60X/5 ( reviews)

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Book Synopsis Dynamical Systems Method and Applications by : Alexander G. Ramm

Download or read book Dynamical Systems Method and Applications written by Alexander G. Ramm. This book was released on 2013-06-07. Available in PDF, EPUB and Kindle. Book excerpt: 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

1994-07-26 Science
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Release : 1994-07-26
Genre : Science
Kind : eBook
Book Rating : 057/5 ( reviews)

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Book Synopsis Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems by : Krzysztof Kowalski

Download or read book Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems written by Krzysztof Kowalski. This book was released on 1994-07-26. Available in PDF, EPUB and Kindle. Book excerpt: 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 Schrödinger-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, Bäcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

2021-07-14 Technology & Engineering
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Release : 2021-07-14
Genre : Technology & Engineering
Kind : eBook
Book Rating : 53X/5 ( reviews)

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Book Synopsis Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems by : Vasile Marinca

Download or read book Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems written by Vasile Marinca. This book was released on 2021-07-14. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.

Nonlinear Dynamical Systems in Engineering

2012-01-05 Technology & Engineering
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Release : 2012-01-05
Genre : Technology & Engineering
Kind : eBook
Book Rating : 341/5 ( reviews)

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Book Synopsis Nonlinear Dynamical Systems in Engineering by : Vasile Marinca

Download or read book Nonlinear Dynamical Systems in Engineering written by Vasile Marinca. This book was released on 2012-01-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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