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Author : Aleksandr Dmitrievic Brjuno
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (916 download)
Download or read book Local Methods of nonlinear differential equations written by Aleksandr Dmitrievic Brjuno and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Aleksandr Dmitrievich Bri͡uno
Publisher : Springer
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)
Download or read book Local Methods in Nonlinear Differential Equations written by Aleksandr Dmitrievich Bri͡uno and published by Springer. This book was released on 1989 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander D. Bruno
Publisher :
ISBN 13 : 9783540189268
Total Pages : 348 pages
Book Rating : 4.1/5 (892 download)
Download or read book Local Methods in Nonlinear Differential Equations written by Alexander D. Bruno and published by . This book was released on 1989-01-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of normal forms is usually attributed to PoincarA(c) although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students.
Author : Dongming Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3764374292
Total Pages : 374 pages
Book Rating : 4.7/5 (643 download)
Download or read book Differential Equations with Symbolic Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Author : Alexander D. Bruno
Publisher : Springer
ISBN 13 : 9783642613142
Total Pages : 0 pages
Book Rating : 4.6/5 (131 download)
Download or read book Local Methods in Nonlinear Differential Equations written by Alexander D. Bruno and published by Springer. This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of normal forms is usually attributed to Poincaré although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students.
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 0821841432
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)
Download or read book Nonlinear Dispersive Equations written by Terence Tao and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Author : Feliz Manuel Minhós
Publisher : MDPI
ISBN 13 : 3036507108
Total Pages : 158 pages
Book Rating : 4.0/5 (365 download)
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Y. N. Bibikov
Publisher : Springer
ISBN 13 : 3540355278
Total Pages : 155 pages
Book Rating : 4.5/5 (43 download)
Download or read book Local Theory of Nonlinear Analytic Ordinary Differential Equations written by Y. N. Bibikov and published by Springer. This book was released on 2006-11-15 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Juan R. Torregrosa
Publisher : MDPI
ISBN 13 : 3039219405
Total Pages : 494 pages
Book Rating : 4.0/5 (392 download)
Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Author : Iı̐Uı̐Łrii Nikolaevich Bibikov
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.3/5 (91 download)
Download or read book Local Theory of Nonlinear Analytic Ordinary Differential Equations written by Iı̐Uı̐Łrii Nikolaevich Bibikov and published by Lecture Notes in Mathematics. This book was released on 1979-02-05 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tran Duc Van
Publisher : CRC Press
ISBN 13 : 9781584880165
Total Pages : 256 pages
Book Rating : 4.8/5 (81 download)
Download or read book The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations written by Tran Duc Van and published by CRC Press. This book was released on 1999-06-25 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.
Author : Alexei Cheviakov
Publisher : Springer Nature
ISBN 13 : 3031530748
Total Pages : 322 pages
Book Rating : 4.0/5 (315 download)
Download or read book Analytical Properties of Nonlinear Partial Differential Equations written by Alexei Cheviakov and published by Springer Nature. This book was released on with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jane Cronin
Publisher : American Mathematical Soc.
ISBN 13 : 0821815113
Total Pages : 212 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fixed points and topological degree in nonlinear analysis written by Jane Cronin and published by American Mathematical Soc.. This book was released on 1995-01-05 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with ``large'' nonlinearities. Then, after being extended to infinite-dimensional ``function-spaces'', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.
Author : Richard E. Ewing
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (227 download)
Download or read book Numerical and Analytical Methods in Nonlinear Partial Differential Equations written by Richard E. Ewing and published by . This book was released on 1987 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex physical phenomena involving chemically reacting systems or the transport of heat or fluids are often modeled by coupled systems of time-dependent, nonlinear partial differential equations. The difficulties in understanding the stability of the differential equation systems and in designing efficient, accurate numerical methods for their solution are widely recognized and were the focus of this research. We have worked on four general aspects of the analysis and numerical approximation of systems of partial differential equations. These areas of research are: (1) modeling aspects and stability analysis for nonlinear time-dependent partial differential equations; (2) use and analysis of finite element or finite difference methods to discretize coupled systems of nonlinear differential equations; (3) development of adaptive or local grid refinement capabilities to resolve local phenomena in large-scale applications; and (4) development of data structures, preconditioners, and efficient solution algorithms for large-scale problems on new computer architectures. Emphasis has been placed upon multiphase or multicomponent, transport-dominated flow processes with dynamic local phenomena. The research also involved a mix of analysis, algorithm development, and large-scale computation using newer computer architectures.
Author : Yihong Du
Publisher : World Scientific
ISBN 13 : 9812774440
Total Pages : 202 pages
Book Rating : 4.8/5 (127 download)
Download or read book Order Structure and Topological Methods in Nonlinear Partial Differential Equations written by Yihong Du and published by World Scientific. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems. The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time. Sample Chapter(s). Chapter 1: Krein-Rutman Theorem and the Principal Eigenvalue (128 KB). Contents: KreinOCoRutman Theorem and the Principal Eigenvalue; Maximum Principles Revisited; The Moving Plane Method; The Method of Upper and Lower Solutions; The Logistic Equation; Boundary Blow-Up Problems; Symmetry and Liouville Type Results Over Half and Entire Spaces. Readership: Researchers and postgraduate students in partial differential equations."
Author : P.A. Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 940112082X
Total Pages : 466 pages
Book Rating : 4.4/5 (11 download)
Download or read book Applications of Analytic and Geometric Methods to Nonlinear Differential Equations written by P.A. Clarkson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.
Author : Bruno Carpentieri
Publisher : BoD – Books on Demand
ISBN 13 : 1839686561
Total Pages : 374 pages
Book Rating : 4.8/5 (396 download)
Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-09-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.
