عنوان

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

(Number (ISBN

3662090171

(Number (ISBN

9783662090176

Number

b580160

Title Proper

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

General Material Designation

[Book]

First Statement of Responsibility

by Willem Hundsdorfer, Jan Verwer.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

2003

Specific Material Designation and Extent of Item

(x, 471 pages)

Series Title

Springer series in computational mathematics, 33.

Text of Note

I Basic Concepts and Discretizations --; II Time Integration Methods --; III Advection-Diffusion Discretizations --; IV Splitting Methods --; V Stabilized Explicit Runge-Kutta Methods.

Text of Note

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.

Differential equations, Partial.

Differential equations.

Mathematics.

Class number

Book number

by Willem Hundsdorfer, Jan Verwer.

Jan Verwer

Willem Hundsdorfer

Electronic name

[Book]

Y