Multiscale Methods Averaging and Homogenization /

• Main Authors: Pavliotis, Grigorios A. (Author), Stuart, Andrew M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2008.
• Series: Texts Applied in Mathematics, 53
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Computer mathematics.; Probabilities.; Physics.; Applied mathematics.; Engineering mathematics.; Analysis.; Partial Differential Equations.; Probability Theory and Stochastic Processes.; Appl.Mathematics/Computational Methods of Engineering.; Mathematical Methods in Physics.; Computational Science and Engineering.

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 poss...

Table of Contents:

• 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.