Numerical Methods and Analysis of Multiscale Problems
Madureira, Alexandre L.
Numerical Methods and Analysis of Multiscale Problems [electronic resource] / by Alexandre L. Madureira. - 1st ed. 2017. - X, 123 p. 31 illus., 9 illus. in color. online resource. - SpringerBriefs in Mathematics, 2191-8198 . - SpringerBriefs in Mathematics, .
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.
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.
9783319508665
10.1007/978-3-319-50866-5 doi
Numerical analysis.
Partial differential equations.
Applied mathematics.
Engineering mathematics.
Numerical Analysis.
Partial Differential Equations.
Applications of Mathematics.
QA297-299.4
518
Numerical Methods and Analysis of Multiscale Problems [electronic resource] / by Alexandre L. Madureira. - 1st ed. 2017. - X, 123 p. 31 illus., 9 illus. in color. online resource. - SpringerBriefs in Mathematics, 2191-8198 . - SpringerBriefs in Mathematics, .
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.
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.
9783319508665
10.1007/978-3-319-50866-5 doi
Numerical analysis.
Partial differential equations.
Applied mathematics.
Engineering mathematics.
Numerical Analysis.
Partial Differential Equations.
Applications of Mathematics.
QA297-299.4
518