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Author: Aleksandr Dmitrievic Brjuno
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Aleksandr Dmitrievic Brjuno
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Aleksandr Dmitrievich Bri͡uno
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Author: Aleksandr Dmitrievic Brjuno
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Feliz Manuel Minhós
Publisher: MDPI
ISBN: 3036507108
Category : Mathematics
Languages : en
Pages : 158
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Book Description
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: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821841432
Category : Mathematics
Languages : en
Pages : 394
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Book Description
"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: Dongming Wang
Publisher: Springer Science & Business Media
ISBN: 3764374292
Category : Mathematics
Languages : en
Pages : 374
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Book Description
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: 9783642613142
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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: Y. N. Bibikov
Publisher: Springer
ISBN: 3540355278
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Author: Juan R. Torregrosa
Publisher: MDPI
ISBN: 3039219405
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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:
Category : Mathematics
Languages : en
Pages : 166
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Book Description
