The Concept of Stability in Numerical Math...

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Sprache: Englisch

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Beschreibung

In this book, the author compares the meaning of stability in different subfields of numerical mathematics.
Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.
In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.

Über den Autor

The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and a book in German about the technique of hierarchical matrices. Hackbusch is also in the editorial board of Springer's book series "Advances in Numerical Mathematics" and "The International Cryogenics Monograph Series".

Zusammenfassung

Offers a self-contained presentation of aspects of stability in numerical mathematics

Compares and characterizes stability in different subfields of numerical mathematics

Covers numerical treatment of ordinary differential equations, discretisation of partial differential equations, discretisation of integral equations and more

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- Introduction.- Stability of Finite Algorithms.- Quadrature.- Interpolation.- Ordinary Differential Equations.- Instationary Partial Difference Equations.- Stability for Discretisations of Elliptic Problems.- Stability for Discretisations of Integral Equations.- Index.

Details

Erscheinungsjahr:	2014
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	204
Reihe:	Springer Series in Computational Mathematics
Inhalt:	xv 188 S.
ISBN-13:	9783642393853
ISBN-10:	3642393853
Sprache:	Englisch
Herstellernummer:	86276945
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Hackbusch, Wolfgang
Auflage:	2014
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Series in Computational Mathematics
Maße:	241 x 160 x 17 mm
Von/Mit:	Wolfgang Hackbusch
Erscheinungsdatum:	20.02.2014
Gewicht:	0,477 kg

preigu-id: 105686570