Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations [electronic resource] /

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.

Bibliographic Details

Main Authors:	Hundsdorfer, Willem. author., Verwer, Jan. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003
Subjects:	Engineering., Differential equations., Partial differential equations., Numerical analysis., Applied mathematics., Engineering mathematics., Appl.Mathematics/Computational Methods of Engineering., Partial Differential Equations., Ordinary Differential Equations., Numerical Analysis.,
Online Access:	http://dx.doi.org/10.1007/978-3-662-09017-6
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