Numerical Methods and Analysis of Multiscale Problems

Nonfiction, Science & Nature, Mathematics, Number Systems, Differential Equations
Cover of the book Numerical Methods and Analysis of Multiscale Problems by Alexandre L. Madureira, Springer International Publishing
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Author: Alexandre L. Madureira ISBN: 9783319508665
Publisher: Springer International Publishing Publication: February 15, 2017
Imprint: Springer Language: English
Author: Alexandre L. Madureira
ISBN: 9783319508665
Publisher: Springer International Publishing
Publication: February 15, 2017
Imprint: Springer
Language: English

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.

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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.

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