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

Abstract

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.