LEADER 03470nam 2200649 450 001 996466626303316 005 20220911152611.0 010 $a3-540-46832-3 024 7 $a10.1007/BFb0093947 035 $a(CKB)1000000000437397 035 $a(SSID)ssj0000325322 035 $a(PQKBManifestationID)12072402 035 $a(PQKBTitleCode)TC0000325322 035 $a(PQKBWorkID)10323845 035 $a(PQKB)11651660 035 $a(DE-He213)978-3-540-46832-5 035 $a(MiAaPQ)EBC5595045 035 $a(Au-PeEL)EBL5595045 035 $a(OCoLC)1076260440 035 $a(MiAaPQ)EBC6842174 035 $a(Au-PeEL)EBL6842174 035 $a(PPN)155176579 035 $a(EXLCZ)991000000000437397 100 $a20220911d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe numerical solution of differential-algebraic systems by Runge-Kutta methods. /$fErnst Hairer, Michel Roche, Christian Lubich 205 $a1st ed. 1989. 210 1$aBerlin, Germany :$cSpringer-Verlag,$d[1989] 210 4$dİ1989 215 $a1 online resource (X, 146 p.) 225 1 $aLecture Notes in Mathematics ;$v1409 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-51860-6 327 $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. 330 $aThe term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1409. 606 $aDifferential-algebraic equations$xNumerical solutions 606 $aNumerical analysis 606 $aRunge-Kutta formulas 615 0$aDifferential-algebraic equations$xNumerical solutions. 615 0$aNumerical analysis. 615 0$aRunge-Kutta formulas. 676 $a511.4 700 $aHairer$b E$g(Ernst),$021071 702 $aLubich$b Christian$f1959- 702 $aRoche$b Michel$f1959- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466626303316 996 $aNumerical solution of differential-algebraic systems by Runge-Kutta Methods$9262315 997 $aUNISA