Multiscale Methods : Averaging and Homogenization

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...

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Main Authors: Pavliotis, Grigoris, Stuart, Andrew (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2008, 2008
Edition:1st ed. 2008
Series:Texts in Applied Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Summary: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.
Physical Description:XVIII, 310 p online resource
ISBN:9780387738291