Abstract
We study the optimal orders of (global and local) superconvergence in piecewise polynomial collocation on quasi-graded meshes for functional differential equations with (nonlinear) delays vanishing at t=0. It is shown that while for linear delays (e.g. proportional delays qt with 0<q<1) and certain nonlinear delays the classical optimal order results still hold, high degree of tangency with the identity function at t=0 leads not only to a reduction in the order of superconvergence but also to very serious difficulties in the actual computation of numerical approximations.
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AMS subject classification (2000)
65R20, 34K28
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Bellen, A., Brunner, H., Maset, S. et al. Superconvergence in Collocation Methods on Quasi-Graded Meshes for Functional Differential Equations with Vanishing Delays. Bit Numer Math 46, 229–247 (2006). https://doi.org/10.1007/s10543-006-0055-2
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DOI: https://doi.org/10.1007/s10543-006-0055-2