Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
W. H. Hundsdorfer (Author), Jan Verwer (Author)
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
eBook, English, 2003
Springer Berlin Heidelberg : Imprint : Springer, Berlin, Heidelberg, 2003
1 online resource (x, 472 pages) : online resource
9783662090176, 3662090171
1159648569
Printed edition:
I Basic Concepts and Discretizations
II Time Integration Methods
III Advection-Diffusion Discretizations
IV Splitting Methods
V Stabilized Explicit Runge-Kutta Methods
Bibliographic Level Mode of Issuance: Monograph
English