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Numerical Methods for Singularly Perturbed Differential Equations
Convection-Diffusion and Flow Problems
Langbeschreibung
This book collects, explains and analyses basic methods and recent results for the successful numerical solution of singularly perturbed differential equations. Such equations model many physical phenomena and their solutions are characterized by the presence of layers. The book is a wide-ranging introduction to the exciting current literature in this area. It concentrates on linear convection-diffusion equations and related nonlinear flow problems, encompassing both ordinary and partial differential equations. While many numerical methods are considered, particular attention is paid to those with realistic error estimates. The book provides a solid and thorough foundation for the numerical analysis and solution of singular perturbation problems.
Inhaltsverzeichnis
I. Ordinary Differential Equations: The analytical behaviour of solutions - numerical methods for second-order boundary value problems - numerical methods for higher-order problems II. Parabolic Initial-Boundary Value Problems in One Space Dimension: Analytical behaviour of solutions - finite difference methods - finite element methods - adaptive methods III. Elliptic Boundary Value Problems: Analytical behaviour of solutions - finite difference methods - finite element methods IV. Incompressible Navier-Stokes Equations: Existence and uniqueness results - an upwind finite element method - stabilized higher order methods - adaptive error control Appendix: Robust Solvers for Linear Systems
ISBN-13:
9783662032060
Veröffentl:
2013
Seiten:
352
Autor:
Hans-Görg Roos
Serie:
24, Springer Series in Computational Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
85,59 €*
Lieferzeit: Sofort lieferbar
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