Description
Numerical Methods and Analysis of Multiscale Problems, 1st ed. 2017
SpringerBriefs in Mathematics Series
Author: Madureira Alexandre L.
Language: English52.74 €
In Print (Delivery period: 15 days).
Add to cart the print on demand of Madureira Alexandre L.Support: Print on demand
Description
/li>Contents
/li>Biography
/li>Comment
/li>
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.
Introductory Material and Finite Element Methods.- A One-dimensional Singular Perturbed Problem.- An Application in Neuroscience: Heterogeneous Cable Equation.- Two-Dimensional Reaction-Diffusion Equations.- Modeling PDEs in Domains with Rough Boundaries.- Partial Differential Equations with Oscillatory Coefficients.
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
Includes supplementary material: sn.pub/extras