Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Series: | Springer Series in Computational Mathematics
33 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs. The first chapter provides a self-contained introduction to the field and can be used for an undergraduate course on the numerical solution of PDEs. The remaining four chapters are more specialized and of interest to researchers, practitioners and graduate students from numerical mathematics, scientific computing, computational physics and other computational sciences |
| Physical Description: | 1 Online-Ressource (X, 472 p) |
| ISBN: | 9783662090176 9783642057076 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-662-09017-6 |
Staff View
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| spelling | Hundsdorfer, Willem Verfasser aut Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by Willem Hundsdorfer, Jan Verwer Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (X, 472 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 33 0179-3632 This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs. The first chapter provides a self-contained introduction to the field and can be used for an undergraduate course on the numerical solution of PDEs. The remaining four chapters are more specialized and of interest to researchers, practitioners and graduate students from numerical mathematics, scientific computing, computational physics and other computational sciences Mathematics Differential Equations Differential equations, partial Numerical analysis Partial Differential Equations Ordinary Differential Equations Numerical Analysis Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Advektion-Diffusionsgleichung (DE-588)4580212-9 gnd rswk-swf Advektion-Diffusionsgleichung (DE-588)4580212-9 s Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Verwer, Jan Sonstige oth https://doi.org/10.1007/978-3-662-09017-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hundsdorfer, Willem Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations Mathematics Differential Equations Differential equations, partial Numerical analysis Partial Differential Equations Ordinary Differential Equations Numerical Analysis Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Advektion-Diffusionsgleichung (DE-588)4580212-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4323967-5 (DE-588)4580212-9 |
| title | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations |
| title_auth | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations |
| title_exact_search | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations |
| title_full | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by Willem Hundsdorfer, Jan Verwer |
| title_fullStr | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by Willem Hundsdorfer, Jan Verwer |
| title_full_unstemmed | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by Willem Hundsdorfer, Jan Verwer |
| title_short | Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations |
| title_sort | numerical solution of time dependent advection diffusion reaction equations |
| topic | Mathematics Differential Equations Differential equations, partial Numerical analysis Partial Differential Equations Ordinary Differential Equations Numerical Analysis Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Advektion-Diffusionsgleichung (DE-588)4580212-9 gnd |
| topic_facet | Mathematics Differential Equations Differential equations, partial Numerical analysis Partial Differential Equations Ordinary Differential Equations Numerical Analysis Mathematik Numerisches Verfahren Reaktions-Diffusionsgleichung Advektion-Diffusionsgleichung |
| url | https://doi.org/10.1007/978-3-662-09017-6 |
| work_keys_str_mv | AT hundsdorferwillem numericalsolutionoftimedependentadvectiondiffusionreactionequations AT verwerjan numericalsolutionoftimedependentadvectiondiffusionreactionequations |