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Rigorous Numerics in Dynamics

2018-07-12 Mathematics
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Release : 2018-07-12
Genre : Mathematics
Kind : eBook
Book Rating : 148/5 ( reviews)

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Book Synopsis Rigorous Numerics in Dynamics by : Jan Bouwe van den Berg

Download or read book Rigorous Numerics in Dynamics written by Jan Bouwe van den Berg. This book was released on 2018-07-12. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures delivered at the 2016 AMS Short Course “Rigorous Numerics in Dynamics”, held January 4–5, 2016, in Seattle, Washington. Nonlinear dynamics shapes the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell. Mathematically these phenomena are modeled by nonlinear dynamical systems, in the form of ODEs, PDEs and delay equations. The presence of nonlinearities complicates the analysis, and the difficulties are even greater for PDEs and delay equations, which are naturally defined on infinite dimensional function spaces. With the availability of powerful computers and sophisticated software, numerical simulations have quickly become the primary tool to study the models. However, while the pace of progress increases, one may ask: just how reliable are our computations? Even for finite dimensional ODEs, this question naturally arises if the system under study is chaotic, as small differences in initial conditions (such as those due to rounding errors in numerical computations) yield wildly diverging outcomes. These issues have motivated the development of the field of rigorous numerics in dynamics, which draws inspiration from ideas in scientific computing, numerical analysis and approximation theory. The articles included in this volume present novel techniques for the rigorous study of the dynamics of maps via the Conley-index theory; periodic orbits of delay differential equations via continuation methods; invariant manifolds and connecting orbits; the dynamics of models with unknown nonlinearities; and bifurcations diagrams.

Rigorous Numerics in Dynamics

2018 Nonlinear mechanics
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Release : 2018
Genre : Nonlinear mechanics
Kind : eBook
Book Rating : 298/5 ( reviews)

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Book Synopsis Rigorous Numerics in Dynamics by : Jan Bouwe Van

Download or read book Rigorous Numerics in Dynamics written by Jan Bouwe Van. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures delivered at the 2016 AMS Short Course ""Rigorous Numerics in Dynamics"", held January 4-5, 2016, in Seattle, Washington. Nonlinear dynamics shapes the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell. Mathematically these phenomena are modeled by nonlinear dynamical systems, in the form of ODEs, PDEs and delay equations. The presence of nonlinearities complicates the analysis, and the difficulties are even greater for PDEs and delay equations, which a.

Handbook of Dynamical Systems

2002-02-21 Science
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Release : 2002-02-21
Genre : Science
Kind : eBook
Book Rating : 845/5 ( reviews)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler. This book was released on 2002-02-21. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Dynamics: Numerical Explorations

2014-03-03 Mathematics
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Release : 2014-03-03
Genre : Mathematics
Kind : eBook
Book Rating : 322/5 ( reviews)

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Book Synopsis Dynamics: Numerical Explorations by : Helena E. Nusse

Download or read book Dynamics: Numerical Explorations written by Helena E. Nusse. This book was released on 2014-03-03. Available in PDF, EPUB and Kindle. Book excerpt: Co-author J.A. Yorke developed an array of tools to help visualize the properties of dynamical systems, while Yorke found it useful to combine these various basic tools into one single package: Dynamics. The program together with this manual provides an introduction to and an overview of fundamental, sophisticated tools and numerical methods together with many simple examples. All numerical methods described in this handbook are implemented in the program, which is capable of, among others: iterating maps and solving differential equations; plotting trajectories; featuring an array of simple commands; printing a created picture in resolution higher than that of the screen. Requires a UNIX workstation running X11 graphics or a PC.

Numerical Methods in Fluid Dynamics

1985-10-31 Mathematics
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Release : 1985-10-31
Genre : Mathematics
Kind : eBook
Book Rating : 248/5 ( reviews)

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Book Synopsis Numerical Methods in Fluid Dynamics by : Gary A. Sod

Download or read book Numerical Methods in Fluid Dynamics written by Gary A. Sod. This book was released on 1985-10-31. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

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