SpringerBriefs in Mathematics

Numerical Methods and Analysis of Multiscale Problems

Authors: Madureira, Alexandre L

  • Offers an introduction to asymptotic analysis techniques and various finite element methods for elliptic problems
  • Presents numerous case studies on modeling techniques of multiscale PDEs, in one- and two-dimensional domains
  • Explores modeling through both continuous and numerical approximations
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eBook $39.99
price for Brazil (gross)
  • ISBN 978-3-319-50866-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Brazil
  • ISBN 978-3-319-50864-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales.  Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses  examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.


About the authors

Alexandre L. Madureira is a senior researcher at the National Laboratory for Scientific Computing (LNCC), Brazil, and also works at the Brazilian School of Economics and Finance (EPGE) at the Fundação Getúlio Vargas (FGV). He holds a PhD from Penn State University, USA, and served as a visiting professor at the Istituto di Analisi Numerica (IAN), Italy, University of Colorado at Denver, USA, and Brown University, USA. His main field of interest is numerical analysis, more specifically modeling and analysis of multiscale problems from PDE and numerical points of view.

Table of contents (6 chapters)

  • Introductory Material and Finite Element Methods

    Madureira, Alexandre L.

    Pages 1-21

  • One-Dimensional Singular Perturbed Problems

    Madureira, Alexandre L.

    Pages 23-38

  • An Application in Neuroscience: Heterogeneous Cable Equation

    Madureira, Alexandre L.

    Pages 39-47

  • Two-Dimensional Reaction-Diffusion Equations

    Madureira, Alexandre L.

    Pages 49-65

  • Modeling PDEs in Domains with Rough Boundaries

    Madureira, Alexandre L.

    Pages 67-84

Buy this book

eBook $39.99
price for Brazil (gross)
  • ISBN 978-3-319-50866-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Brazil
  • ISBN 978-3-319-50864-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Methods and Analysis of Multiscale Problems
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-50866-5
DOI
10.1007/978-3-319-50866-5
Softcover ISBN
978-3-319-50864-1
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 123
Number of Illustrations and Tables
22 b/w illustrations, 9 illustrations in colour
Topics