InitDAE: computation of consistent values, index determination and diagnosis of singularities of DAEs using automatic differentiation in Python. (English) Zbl 1458.65163
Summary: InitDAE is a prototype written in Python that computes consistent initial values of differential-algebraic equations (DAE), determines their index and a related condition number that permits the diagnosis of singularities. The algorithm for the consistent initialization uses a projector based constrained optimization approach and the inherent differentiations are provided by automatic differentiation (AD), using AlgoPy. Consequently, a detailed description of the local structural properties of the DAE becomes possible using the SVD. InitDAE has been conceived for academic purposes and is well-suited for examples of moderate size. In this article we give an overview of the algorithm, show actual features and discuss future possibilities, in particular the integration with Taylor series methods.
MSC:
| 65L80 | Numerical methods for differential-algebraic equations |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 65D25 | Numerical differentiation |
| 65-04 | Software, source code, etc. for problems pertaining to numerical analysis |
Keywords:
differential-algebraic equation; consistent initial value problem; numerical integration; nonlinear constrained optimization; automatic differentiationReferences:
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