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Numerical Methods and Analysis of Multiscale Problems / by Alexandre L. Madureira.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Madureira, Alexandre L., Author.
- Series:
- SpringerBriefs in Mathematics, 2191-8198
- Language:
- English
- Subjects (All):
- Numerical analysis.
- Differential equations, Partial.
- Applied mathematics.
- Engineering mathematics.
- Numerical Analysis.
- Partial Differential Equations.
- Applications of Mathematics.
- Local Subjects:
- Numerical Analysis.
- Partial Differential Equations.
- Applications of Mathematics.
- Physical Description:
- 1 online resource (X, 123 p. 31 illus., 9 illus. in color.)
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2017.
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 3-319-50866-0
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