The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
Hairer, Ernst.
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / by Ernst Hairer, Michel Roche, Christian Lubich. - X, 146 p. online resource. - Lecture Notes in Mathematics, 1409 0075-8434 ; . - Lecture Notes in Mathematics, 1409 .
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.
9783540468325
10.1007/BFb0093947 doi
Numerical analysis.
Numerical Analysis.
QA297-299.4
518
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / by Ernst Hairer, Michel Roche, Christian Lubich. - X, 146 p. online resource. - Lecture Notes in Mathematics, 1409 0075-8434 ; . - Lecture Notes in Mathematics, 1409 .
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.
9783540468325
10.1007/BFb0093947 doi
Numerical analysis.
Numerical Analysis.
QA297-299.4
518