Superconvergence in Collocation Methods on Quasi-Graded Meshes for Functional Differential Equations with Vanishing Delays |
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| Authors: | A Bellen H Brunner S Maset L Torelli |
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| Institution: | (1) Dipartimento di Matematica e Informatica, Università di Trieste, I-34127 Trieste, Italy;(2) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7 |
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| 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.
AMS subject classification (2000) 65R20, 34K28 |
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| Keywords: | functional differential equations Volterra integro-differential equations vanishing delays collocation methods quasi-graded meshes optimal order of superconvergence order reduction |
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