Signature method based regularization and numerical integration of differential-algebraic equations
Modeling and simulation of dynamical systems often leads to differential-algebraic equations (DAEs) which can be seen as differential equations, where every solution has to satisfy constraints which are contained in the DAE. In general not all these constraints are stated explicitly as equations or can be obtained by algebraic manipulations but are hidden in the DAE and can be obtained from certain derivatives of (parts of) the DAE. Due to those hidden constraints a direct numerical integration of DAEs in general leads to instabilities and possibly non-convergence of numerical methods. Therefore, a regularization or remodeling of the model equations is required. In this article we present three approaches for the regularization of DAEs that are based on the Signature method, which is a structural analysis for DAEs. Furthermore, we present a software package suited for the proposed regularizations and illustrate their efficiency on two examples.
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