03470nam 2200649 450 99646662630331620220911152611.03-540-46832-310.1007/BFb0093947(CKB)1000000000437397(SSID)ssj0000325322(PQKBManifestationID)12072402(PQKBTitleCode)TC0000325322(PQKBWorkID)10323845(PQKB)11651660(DE-He213)978-3-540-46832-5(MiAaPQ)EBC5595045(Au-PeEL)EBL5595045(OCoLC)1076260440(MiAaPQ)EBC6842174(Au-PeEL)EBL6842174(PPN)155176579(EXLCZ)99100000000043739720220911d1989 uy 0engurnn|008mamaatxtccrThe numerical solution of differential-algebraic systems by Runge-Kutta methods. /Ernst Hairer, Michel Roche, Christian Lubich1st ed. 1989.Berlin, Germany :Springer-Verlag,[1989]©19891 online resource (X, 146 p.) Lecture Notes in Mathematics ;1409Bibliographic Level Mode of Issuance: Monograph3-540-51860-6 Description 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.The 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.Lecture notes in mathematics (Springer-Verlag) ;1409.Differential-algebraic equationsNumerical solutionsNumerical analysisRunge-Kutta formulasDifferential-algebraic equationsNumerical solutions.Numerical analysis.Runge-Kutta formulas.511.4Hairer E(Ernst),21071Lubich Christian1959-Roche Michel1959-MiAaPQMiAaPQMiAaPQBOOK996466626303316Numerical solution of differential-algebraic systems by Runge-Kutta Methods262315UNISA