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Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments

✍ Scribed by Qiya Hu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 119 KB
Volume: 31
Category: Article
ISSN: 0168-9274
DOI: 10.1016/s0168-9274(98)00127-5

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✦ Synopsis

In this paper we give a complete analysis of convergence acceleration method for discrete collocation solutions of Volterra integral equations with constant delay. It will be shown that, when continuous piecewise polynomials of degree m 2 are used, and collocation is based on the Lobatto points, this discrete collocation approximation admits, at the knots, an error expansion in even powers of the step-size h, beginning with a term in h 2m . Based on this expansion we show that, when a correction procedure is applied to such discrete collocation approximation for k times, the global accuracy of the corresponding corrected approximation will be increased to O(h 2m(k+1) ).

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