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Convergence analysis of least-squares collocation methods for nonlinear higher-index differential-algebraic equations. (English) Zbl 1458.65104
Summary: 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.
MSC:
65L80 Numerical methods for differential-algebraic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
Software:
NewtonLib; COLNEW
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