TY - BOOK
AU - Pavliotis,Grigorios A.
AU - Stuart,Andrew M.
ED - SpringerLink (Online service)
TI - Multiscale Methods: Averaging and Homogenization
T2 - Texts Applied in Mathematics,
SN - 9780387738291
AV - QA299.6-433
U1 - 515 23
PY - 2008///
CY - New York, NY
PB - Springer New York
KW - Mathematics
KW - Mathematical analysis
KW - Analysis (Mathematics)
KW - Partial differential equations
KW - Computer mathematics
KW - Probabilities
KW - Physics
KW - Applied mathematics
KW - Engineering mathematics
KW - Analysis
KW - Partial Differential Equations
KW - Probability Theory and Stochastic Processes
KW - Appl.Mathematics/Computational Methods of Engineering
KW - Mathematical Methods in Physics
KW - Computational Science and Engineering
N1 - 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
N2 - 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.
UR - http://dx.doi.org/10.1007/978-0-387-73829-1
ER -