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Sprache: Englisch
Verlag: Springer, Berlin, Springer, 2017
ISBN 10: 3319619330 ISBN 13: 9783319619330
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
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Taschenbuch. Zustand: Neu. Attractors Under Discretisation | Xiaoying Han (u. a.) | Taschenbuch | xi | Englisch | 2017 | Springer | EAN 9783319619330 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Sprache: Englisch
Verlag: World Scientific Pub Co Inc, 2023
ISBN 10: 9811267758 ISBN 13: 9789811267758
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Sprache: Englisch
Verlag: World Scientific Publishing Company, 2023
ISBN 10: 9811267758 ISBN 13: 9789811267758
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Taschenbuch. Zustand: Neu. Random Ordinary Differential Equations and Their Numerical Solution | Xiaoying Han (u. a.) | Taschenbuch | Probability Theory and Stochastic Modelling | xvii | Englisch | 2018 | Springer | EAN 9789811348433 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Sprache: Englisch
Verlag: World Scientific Pub Co Inc, 2023
ISBN 10: 9811267758 ISBN 13: 9789811267758
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In den WarenkorbHardcover. Zustand: Brand New. 380 pages. 9.61x6.69x0.88 inches. In Stock.
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.
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In den WarenkorbHardcover. Zustand: Brand New. 250 pages. 9.25x6.25x0.75 inches. In Stock.