000 03257nam a22004815i 4500
001 978-3-540-46832-5
003 DE-He213
005 20190213151736.0
007 cr nn 008mamaa
008 121227s1989 gw | s |||| 0|eng d
020 _a9783540468325
_9978-3-540-46832-5
024 7 _a10.1007/BFb0093947
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aPBKS
_2thema
082 0 4 _a518
_223
100 1 _aHairer, Ernst.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
_h[electronic resource] /
_cby Ernst Hairer, Michel Roche, Christian Lubich.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1989.
300 _aX, 146 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1409
505 0 _aDescription of differential-algebraic problems -- Runge-Kutta methods for differential-algebraic equations -- Convergence for index 1 problems -- Convergence for index 2 problems -- Order conditions of Runge-Kutta methods for index 2 systems -- Convergence for index 3 problems -- Solution of nonlinear systems by simplified Newton -- Local error estimation -- Examples of differential-algebraic systems and their solution.
520 _aThe term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
650 0 _aNumerical analysis.
650 1 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
700 1 _aRoche, Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLubich, Christian.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662194782
776 0 8 _iPrinted edition:
_z9783540518600
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1409
856 4 0 _uhttps://doi.org/10.1007/BFb0093947
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11728
_d11728