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Multiscale Methods

Averaging and Homogenization

  • Textbook
  • © 2008

Overview

Authors:
  1. Grigorios A. Pavliotis

    1. Department of Mathematics, Imperial College London, London, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  2. Andrew M. Stuart

    1. Mathematics Institute, University of Warwick, Coventry, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  • Hot area in applied mathematics
  • Authors are two of the leading applied mathematicians on multiscale methods
  • Nice overview of theory and application with example and excercises included.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Applied Mathematics (TAM)

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Table of contents (21 chapters)

  1. Theory

    1. Averaging for Markov Chains: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 245-248

    2. Averaging for SDEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 249-253

    3. Homogenization for SDEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 255-262

    4. Homogenization for Elliptic PDEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 263-272

    5. Homogenization for Elliptic PDEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 273-278

    6. Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 279-285

  2. Back Matter

    Pages 287-307
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Keywords

About this book

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and s- bolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook - ries is to meet the current and future needs of these advances and to encourage the teaching of new couses. TAM will publish textbooks suitable for use in advanced undergraduate and - ginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research-level mo- graphs. Pasadena, California J.E. Marsden New York, New York L. Sirovich College Park, Maryland S.S. Antman To my parentsA????? and?o?????? and to my brother?????o. Carry Home.????o???. For my children Natalie, Sebastian, and Isobel.

Reviews

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)

Authors and Affiliations

  • Department of Mathematics, Imperial College London, London, United Kingdom

    Grigorios A. Pavliotis

  • Mathematics Institute, University of Warwick, Coventry, United Kingdom

    Andrew M. Stuart

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