Skip to main content
SpringerLink
Log in
Book cover

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

  • Book
  • © 2003

Overview

Authors:
  1. Willem Hundsdorfer

    1. Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Jan Verwer
    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Monograph on topic with strong importance for applications
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Basic Concepts and Discretizations

    • Willem Hundsdorfer, Jan Verwer
    Pages 1-138

  3. Time Integration Methods

    • Willem Hundsdorfer, Jan Verwer
    Pages 139-214

  4. Advection-Diffusion Discretizations

    • Willem Hundsdorfer, Jan Verwer
    Pages 215-323

  5. Splitting Methods

    • Willem Hundsdorfer, Jan Verwer
    Pages 325-417

  6. Stabilized Explicit Runge-Kutta Methods

    • Willem Hundsdorfer, Jan Verwer
    Pages 419-445

  7. Back Matter

    Pages 447-471
    Download chapter PDF
Back to top

Keywords

About this book

This book deals with numerical methods for solving partial differential equa­ tions (PDEs) coupling advection, diffusion and reaction terms, with a focus on time-dependency. A combined treatment is presented of methods for hy­ perbolic problems, thereby emphasizing the one-way wave equation, meth­ ods for parabolic problems and methods for stiff and non-stiff ordinary dif­ ferential equations (ODEs). With regard to time-dependency we have at­ tempted to present the algorithms and the discussion of their properties for the three different types of differential equations in a unified way by using semi-discretizations, i. e. , the method of lines, whereby the PDE is trans­ formed into an ODE by a suitable spatial discretization. In addition, for hy­ perbolic problems we also discuss discretizations that use information based on characteristics. Due to this combination of methods, this book differs substantially from more specialized textbooks that deal exclusively with nu­ merical methods for either PDEs or ODEs. We treat integration methods suitable for both classes of problems. This combined treatment offers a clear advantage. On the one hand, in the field of numerical ODEs highly valuable methods and results exist which are of practical use for solving time-dependent PDEs, something which is often not fully exploited by numerical PDE researchers. Although many problems can be solved by Euler's method or the Crank-Nicolson method, better alter­ natives are often available which can significantly reduce the computational effort needed to solve practical problems.

Reviews

From the reviews:

"The numerical solution of time-dependent advection-diffusion-reaction problems draws on different areas of numerical analysis … . We appreciate that the quite thorough, yet not pedantic, analytic part of the presentation is intimately interwoven with numerical tests and examples which will enable the reader to judge on the relative merits of the various approaches and really aid him in developing proper software for the problem at hand." (H. Mutsham, Monatshefte für Mathematik, Vol. 144 (2), 2005)

"Let me say at the outset that I highly recommend this book to practitioners … end-users, and those new to the field. One of its strengths is its in-depth presentation of temporal and spatial discretizations and their interaction … . With each topic, key theoretical results are presented. … I found the present authors’ choice of problems to be one of the highlights of the book." (Peter Moore, SIAM Review, Vol. 46 (3), 2004)

"This excellent research monograph contains a comprehensive discussion of numerical techniques for advection-reaction-diffusion partial differential equations (PDEs). The emphasis is on a method of lines approach, the analysis is careful and complete, and the numerical tests designed to verify the theoretical discussions of stability, convergence, monotonicity, etc. involve solving ‘real life’ equations. … As is to be expected in such a carefully prepared monograph, there is an extensive bibliography and a good index. Highly recommended." (Ian Gladwell, Mathematical Reviews, 2004 g)

"The information, densely packed on roughly 450 pages, is abundant though well-structured, smoothly readable, and with emphasis on explanation of key concepts by means of examples that are stripped from unnecessary complications. … a serious student with a hands-on attitude finds in this book an excellent source for self-studies and investigation. … It is a valuable contribution to theSpringer Series in this field of research." (J. Brandts, Nieuw Archief voor Wiskunde, Vol. 7 (1), 2006)

Authors and Affiliations

  • Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

    Willem Hundsdorfer

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation