How AD can help solve differential-algebraic equations
| Autor: | Xiao Li, John D. Pryce, Guangning Tan, Nedialko S. Nedialkov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Control and Optimization
Automatic differentiation Applied Mathematics Ode Numerical Analysis (math.NA) 010103 numerical & computational mathematics Solver Symbolic computation 01 natural sciences Regularization (mathematics) Mechanical system symbols.namesake 0103 physical sciences FOS: Mathematics symbols Applied mathematics Mathematics - Numerical Analysis 010307 mathematical physics 0101 mathematics Differential algebraic equation Software Lagrangian Mathematics |
| Zdroj: | Optimization Methods and Software. 33:729-749 |
| ISSN: | 1029-4937 1055-6788 |
| DOI: | 10.1080/10556788.2018.1428605 |
| Popis: | A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of\ud their equations with respect to time, as part of the so-called index reduction or regularization, to prepare\ud them for numerical solution. This is often done with the help of a computer algebra system. We show\ud in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the\ud Dummy Derivatives method; here we give a mainly theoretical description, with tutorial examples. The\ud second is the solution of a mechanical system directly from its Lagrangian formulation. Here, we outline\ud the theory and show several non-trivial examples of using the ‘Lagrangian facility’ of the Nedialkov–\ud Pryce initial-value solver DAETS, namely a spring-mass-multi-pendulum system; a prescribed-trajectory\ud control problem; and long-time integration of a model of the outer planets of the solar system, taken from\ud the DETEST testing package for ODE solvers. |
| Databáze: | OpenAIRE |
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