Numerical Methods and Analysis of Multiscale Problems
(SpringerBriefs in Mathematics) by Alexandre L.
English | 16 Mar. 2017 | ISBN: 3319508644 | 123 Pages |
PDF | 2.83 MB
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 â€“ or researchers seeking a no - nonsense
approach â€“, 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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