Grigoris Pavliotis, Andrew Stuart

Multiscale Methods (eBook, PDF)

Averaging and Homogenization

• Format: PDF

Produktbeschreibung

This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions.

The presentation of the material is particularly suited to the range of mathematicians, scientists and engineers who want to exploit multiscale methods in applications. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable readers to build their own skills and put them into practice.

Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter. All of the twenty-one chapters are supplemented with exercises.

Grigorios Pavliotis is a Lecturer of Mathematics at Imperial College London.

Andrew Stuart is a Professor of Mathematics at Warwick University.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 310
• Erscheinungstermin: 18. Januar 2008
• Englisch
• ISBN-13: 9780387738291
• Artikelnr.: 43728858

Inhaltsangabe

Background.- Analysis.- Probability Theory and Stochastic Processes.- Ordinary Differential Equations.- Markov Chains.- Stochastic Differential Equations.- Partial Differential Equations.- Perturbation Expansions.- Invariant Manifolds for ODEs.- Averaging for Markov Chains.- Averaging for ODEs and SDEs.- Homogenization for ODEs and SDEs.- Homogenization for Elliptic PDEs.- Homogenization for Parabolic PDEs.- Averaging for Linear Transport and Parabolic PDEs.- Theory.- Invariant Manifolds for ODEs: The Convergence Theorem.- Averaging for Markov Chains: The Convergence Theorem.- Averaging for SDEs: The Convergence Theorem.- Homogenization for SDEs: The Convergence Theorem.- Homogenization for Elliptic PDEs: The Convergence Theorem.- Homogenization for Elliptic PDEs: The Convergence Theorem.- Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem.

Rezensionen

From the reviews: "The book is devoted to introduce problems in which different scales may appear. The value of the book is that a wide class of problems is presented and consequently different techniques used to attack these problems are shown. The book is divided in three different parts. ... it can be used as a handbook for the arguements treated in the sequel." (Fabio Paronetto, Zentralblatt MATH, Vol. 1160, 2009)