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＜電子ブック＞
Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations / by Willem Hundsdorfer, Jan G. Verwer
(Springer Series in Computational Mathematics. ISSN:21983712 ; 33)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	X, 472 p : online resource
著者標目	*Hundsdorfer, Willem author Verwer, Jan G author SpringerLink (Online service)
件　名	LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Differential equations LCSH:Numerical analysis FREE:Mathematical and Computational Engineering Applications FREE:Differential Equations FREE:Numerical Analysis
一般注記	I Basic Concepts and Discretizations -- II Time Integration Methods -- III Advection-Diffusion Discretizations -- IV Splitting Methods -- V Stabilized Explicit Runge-Kutta Methods 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 HTTP:URL=https://doi.org/10.1007/978-3-662-09017-6

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