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Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations

  • Willem Hundsdorfer
  • Jan Verwer

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 33)

Table of contents

  1. Front Matter
    Pages I-X
  2. Willem Hundsdorfer, Jan Verwer
    Pages 1-138
  3. Willem Hundsdorfer, Jan Verwer
    Pages 139-214
  4. Willem Hundsdorfer, Jan Verwer
    Pages 215-323
  5. Willem Hundsdorfer, Jan Verwer
    Pages 325-417
  6. Willem Hundsdorfer, Jan Verwer
    Pages 419-445
  7. Back Matter
    Pages 447-471

About this book

Introduction

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.

Keywords

Evolution Equations Numerical Integration Numerical Mathematics Partial Differential Equations Transport-Chemistry Problems numerical methods partial differential equation

Authors and affiliations

  • Willem Hundsdorfer
    • 1
  • Jan Verwer
  1. 1.Center for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-09017-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05707-6
  • Online ISBN 978-3-662-09017-6
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site