---

＜電子ブック＞
Multiscale Methods : Averaging and Homogenization / by Grigoris Pavliotis, Andrew Stuart
(Texts in Applied Mathematics. ISSN:21969949)

版	1st ed. 2008.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XVIII, 310 p : online resource
著者標目	*Pavliotis, Grigoris author Stuart, Andrew author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Differential equations LCSH:Probabilities LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Mathematical physics LCSH:Mathematics -- Data processing  全ての件名で検索 FREE:Analysis FREE:Differential Equations FREE:Probability Theory FREE:Mathematical and Computational Engineering Applications FREE:Mathematical Methods in Physics FREE:Computational Science and Engineering
一般注記	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 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. HTTP:URL=https://doi.org/10.1007/978-0-387-73829-1

 類似資料