Summary
A procedure is given that generates characterizations of singular manifolds for mildly nonlinear mappings between Banach spaces. This characterization is used to develop a method for determining generalized turning points by using projection methods as a discretization. Applications are given to parameter dependent two-point boundary value problems. In particular, collocation at Gauss points is shown to achieve superconvergence in approximating the parameter at simple turning points.
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Griewank, A., Reddien, G.W. The approximation of generalized turning points by projection methods with superconvergence to the critical parameter. Numer. Math. 48, 591–606 (1986). https://doi.org/10.1007/BF01389452
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DOI: https://doi.org/10.1007/BF01389452