The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

1. Front Matter

   Pages I-VII

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2. Description of differential-algebraic problems

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 1-13

3. Runge-Kutta methods for differential-algebraic equations

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 14-22

4. Convergence for index 1 problems

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 23-29

5. Convergence for index 2 problems

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 30-54

6. Order conditions of Runge-Kutta methods for index 2 systems

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 55-70

7. Convergence for index 3 problems

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 71-91

8. Solution of nonlinear systems by simplified Newton

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 92-98

9. Local error estimation

   • Ernst Hairer, Michel Roche, Christian Lubich

   Pages 99-105

10. Examples of differential-algebraic systems and their solution

    • Ernst Hairer, Michel Roche, Christian Lubich

    Pages 106-123

11. Back Matter

    Pages 124-139

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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.

• Nonlinear system
• Simula
• algebra
• behavior
• control
• convergence
• differential equation
• implementation
• kinetics
• network
• networks
• numerical method
• online
• ordinary differential equation
• simulation

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