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2008 | Buch

Multiscale Methods

Averaging and Homogenization

verfasst von: Grigorios A. Pavliotis, Andrew M. Stuart

Verlag: Springer New York

Buchreihe : Texts in Applied Mathematics

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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.

Inhaltsverzeichnis

Frontmatter

Introduction

Frontmatter
1. Introduction
Grigorios A. Pavliotis, Andrew M. Stuart

Background

Frontmatter
2. Analysis
Grigorios A. Pavliotis, Andrew M. Stuart
3. Probability Theory and Stochastic Processes
Grigorios A. Pavliotis, Andrew M. Stuart
4. Ordinary Differential Equations
Grigorios A. Pavliotis, Andrew M. Stuart
5. Markov Chains
Grigorios A. Pavliotis, Andrew M. Stuart
6. Stochastic Differential Equations
Grigorios A. Pavliotis, Andrew M. Stuart
7. Partial Differential Equations
Grigorios A. Pavliotis, Andrew M. Stuart

Perturbation Expansions

Frontmatter
8. Invariant Manifolds for ODEs
Grigorios A. Pavliotis, Andrew M. Stuart
9. Averaging for Markov Chains
Grigorios A. Pavliotis, Andrew M. Stuart
10. Averaging for ODEs and SDEs
Grigorios A. Pavliotis, Andrew M. Stuart
11. Homogenization for ODEs and SDEs
Grigorios A. Pavliotis, Andrew M. Stuart
12. Homogenization for Elliptic PDEs
Grigorios A. Pavliotis, Andrew M. Stuart
13. Homogenization for Parabolic PDEs
Grigorios A. Pavliotis, Andrew M. Stuart
14. Averaging for Linear Transport and Parabolic PDEs
Grigorios A. Pavliotis, Andrew M. Stuart

Theory

Frontmatter
15. Invariant Manifolds for ODEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
16. Averaging for Markov Chains: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
17. Averaging for SDEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
18. Homogenization for SDEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
19. Homogenization for Elliptic PDEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
20. Homogenization for Elliptic PDEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
21. Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem
Grigorios A. Pavliotis, Andrew M. Stuart
Backmatter
Metadaten
Titel
Multiscale Methods
verfasst von
Grigorios A. Pavliotis
Andrew M. Stuart
Copyright-Jahr
2008
Verlag
Springer New York
Electronic ISBN
978-0-387-73829-1
Print ISBN
978-0-387-73828-4
DOI
https://doi.org/10.1007/978-0-387-73829-1

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