×

Solvability of general differential algebraic equations. (English) Zbl 0821.34005

Summary: In the last few years there has been considerable research on differential algebraic equations (DAE) \(f(t,x,x') = 0\) where \(f_{x'}\) is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable. More recently there have been existence results developed using differential geometry. For complex higher index systems these characterizations can be hard to verify in practice. In this paper the computational verification of solvability is investigated. This first requires developing an alternative set of sufficient conditions for solvability which are more amenable to computation. Verification of these conditions using readily available numerical and symbolic software is then discussed. An example from robotics where classical graph theoretical approaches give an incorrect answer is worked to illustrate the usefulness of the sufficient condition and the computational approach.

MSC:

34A09 Implicit ordinary differential equations, differential-algebraic equations
65H10 Numerical computation of solutions to systems of equations
65L08 Numerical solution of ill-posed problems involving ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI