Willem Hundsdorfer, Jan G. Verwer

eBook, PDF

Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations (eBook, PDF)

Beschreibung

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 is on time-dependent transport-chemistry problems. 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. 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.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 44.23MB

Barrierefreiheit

• Text-to-Speech

Autor

Willem Hundsdorfer, Center for Mathematics & Computer Science (CWI), Amsterdam, The Netherlands / Jan G. Verwer, Center for Mathematics & Computer Science (CWI), Amsterdam, The Netherlands

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 472
• Erscheinungstermin: 17. April 2013
• Englisch
• ISBN-13: 9783662090176
• Artikelnr.: 53393257

Rezensionen

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 the Springer Series in this field of research." (J. Brandts, Nieuw Archief voor Wiskunde, Vol. 7 (1), 2006)