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＜E-Book＞
The Concept of Stability in Numerical Mathematics / by Wolfgang Hackbusch
(Springer Series in Computational Mathematics. ISSN:21983712 ; 45)

Edition	1st ed. 2014.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2014
Language	English
Size	XV, 188 p : online resource
Authors	*Hackbusch, Wolfgang author SpringerLink (Online service)
Subjects	LCSH:Numerical analysis LCSH:Differential equations LCSH:Integral equations FREE:Numerical Analysis FREE:Differential Equations FREE:Integral Equations
Notes	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 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.   HTTP:URL=https://doi.org/10.1007/978-3-642-39386-0

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