Convergence analysis of least-squares collocation methods for nonlinear higher-index differential–algebraic equations

We approach 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 and the numerical experiments show promising results. Nevertheless, the theoretical basic concept turns out to be considerably challenging. So far, quite recently, convergence proofs have been published for linear problems. In the present paper we come up with a first basic qualitative convergence result for nonlinear problems.