Multiscale methods : averaging and homogenization
著者
書誌事項
Multiscale methods : averaging and homogenization
（Texts in applied mathematics, 53）
Springer, c2008
- : hbk
- : e-book
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This introduction to multiscale methods gives you a broad overview of the methods' many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your 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.With the exception of Chapter One, all chapters are supplemented with exercises.
目次
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.
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