A least-squares collocation method for nonlinear higher-index differential-algebraic equations
This work addresses the challenging problem of numerically solving nonlinear higher-index DAEs, offering a practical method with theoretical backing for researchers in numerical analysis.
The paper presents a least-squares collocation method for solving nonlinear higher-index differential-algebraic equations, achieving impressive numerical results with computational cost similar to standard collocation methods for ODEs. It provides the first convergence proof for nonlinear problems.
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard collocation methods for regular ordinary differential equations. The numerical experiments show impressive results. In contrast, the theoretical basic concept turns out to be considerably challenging. So far, quite recently convergence proofs for linear problems have been published. In the present paper we come up to a first convergence result for nonlinear problems.