Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

Preface; 1. Introduction: why DAE's?; Basic types of DAE's; applications; Overview; 2. Theory of DAE's; Iintroduction; solvability and the index; Linear constant coefficient DAE's; Linear time varying DAE's; Nonlinear systems; 3. Multistep methods; Introduction; DBF convergence; BDF methods, DAE's and stiff problems; General linear multistep methods; 4. One-step methods; Introduction; Linear constant coefficient systems; Nonlinear index one systems; Semi-Explicit Nonlinear Index Two systems; Order reduction and stiffness; Extrapolation Methods; 5. Software and DAE's; Introduction; Algorithms and Strategies in Dassl; Obtaining numerical solutions; Solving higher index systems; 6. Applications. Introduction; Systems of rigid bodies; Trajectory prescribed path control; Electrical networks; DAE's arising from the method of lines; Bibliography; 7. The DAE home page; Introduction; theoretical advances; Numerical analysis advancements; DAE software; DASSL; Supplementary bibliography; Index.