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100   $a20140206d2014      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe concept of stability in numerical mathematics /$fby Wolfgang Hackbusch
205   $a1st ed. 2014.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014.
215   $a1 online resource (202 pages) $cillustrations
225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v45
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-39385-3 
320   $aIncludes bibliographical references at the end of each chapters and index.
327   $aPreface -- 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.
330   $aIn this book, the author compares the meaning of stability in different subfields of numerical mathematics.  Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.  .
410  0$aSpringer Series in Computational Mathematics,$x0179-3632 ;$v45
606   $aNumerical analysis
606   $aPartial differential equations
606   $aIntegral equations
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090
615  0$aNumerical analysis.
615  0$aPartial differential equations.
615  0$aIntegral equations.
615 14$aNumerical Analysis.
615 24$aPartial Differential Equations.
615 24$aIntegral Equations.
676   $a518
700   $aHackbusch$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$051792
906   $aBOOK
912   $a9910300144603321
996   $aConcept of stability in numerical mathematics$9821048
997   $aUNINA