03491nam 22006135 450 991030014460332120220415201226.03-642-39386-110.1007/978-3-642-39386-0(CKB)3710000000088130(SSID)ssj0001175781(PQKBManifestationID)11760502(PQKBTitleCode)TC0001175781(PQKBWorkID)11139841(PQKB)10073408(MiAaPQ)EBC1697966(DE-He213)978-3-642-39386-0(PPN)176748202(EXLCZ)99371000000008813020140206d2014 u| 0engurcnu||||||||txtccrThe concept of stability in numerical mathematics[electronic resource] /by Wolfgang Hackbusch1st ed. 2014.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2014.1 online resource (202 pages) illustrationsSpringer Series in Computational Mathematics,0179-3632 ;45Bibliographic Level Mode of Issuance: Monograph3-642-39385-3 Includes bibliographical references at the end of each chapters and index.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.  .Springer Series in Computational Mathematics,0179-3632 ;45Numerical analysisPartial differential equationsIntegral equationsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Numerical analysis.Partial differential equations.Integral equations.Numerical Analysis.Partial Differential Equations.Integral Equations.518Hackbusch Wolfgangauthttp://id.loc.gov/vocabulary/relators/aut51792BOOK9910300144603321Concept of stability in numerical mathematics821048UNINA