Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations

Abstract

In modeling and simulation of dynamical processes frequently higher index differential-algebraic equations (DAEs) arise. Since an attempt to solve higher-index DAEs directly yields several numerical problems, a regularization in combination with a robust and efficient integration is required. QUALIDAES is a DAE solver designed to make explicit use of such a regularization. It allows for the solution of over-determined quasi-linear DAEs of the form M(x,t)ẋ = f (x,t), 0 = g(x,t). Such DAEs arise naturally if a quasi-linear DAE is regularized by augmentation with the set of its (hidden) constraints. General DAEs can be brought into the quasi-linear form. To this end, equations can be transformed into the specific input format expected by QUALIDAES. This transformation can be implemented in a functional style and yields a non-trivial result. Additionally it provides an onthe-fly solution for the occurrence of higher-order derivatives.