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We introduce a direct numerical treatment of nonlinear higher-indexdifferential-algebraic equations by means of overdetermined polynomialleast-squares collocation. The procedure is not much more computationallyexpensive than standard collocation methods for regular ordinary differentialequations. The numerical experiments show impressive results. In contrast, thetheoretical basic concept turns out to be considerably challenging. So far,quite recently convergence proofs for linear problems have been published. Inthe present paper we come up to a first convergence result for nonlinearproblems.

A least-squares collocation method for nonlinear higher-index differential-algebraic equations