We study the optimal order of (global and local) superconvergence of 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 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.

Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays.

BELLEN, ALFREDO;MASET, STEFANO;TORELLI, LUCIO
2006-01-01

Abstract

We study the optimal order of (global and local) superconvergence of 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
2006
BIT
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1690038
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