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[null,"1.","Record Nr.",null,"UNISA996466626303316"]
[null,null,"Autore",null,"Hairer E (Ernst)"]
[null,null,"Titolo",null,"The numerical solution of differential-algebraic systems by Runge-Kutta methods. / / Ernst Hairer, Michel Roche, Christian Lubich"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Germany : , : Springer-Verlag, , [1989]"]
[{"$nulls":4},"©1989"]
[null,null,"ISBN",null,"3-540-46832-3"]
[null,null,"Edizione",null,"[1st ed. 1989.]"]
[null,null,"Descrizione fisica",null,"1 online resource (X, 146 p.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics ; ; 1409"]
[null,null,"Disciplina",null,"511.4"]
[null,null,"Soggetti",null,"Differential-algebraic equations - Numerical solutions"]
[{"$nulls":4},"Numerical analysis"]
[{"$nulls":4},"Runge-Kutta formulas"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","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."]