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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Analysis of collocation solutions for a class of functional equations with vanishing delays

Language

English

Abstract

We study the existence, uniqueness and regularity properties of solutions for the functional equation y(t) = b(t)y(θ(t)) + f(t), t ∈ [0, T], where the delay function θ(t) vanishes at t = 0. Functional equations corresponding to the linear delay function θ(t) = qt (0 < q < 1) represent an important special case. We then analyse the optimal order of convergence of piecewise polynomial collocation approximations to solutions of these functional equations. The theoretical results are illustrated by extensive numerical examples. © The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Keywords

collocation solutions, functional equation with vanishing delay, integro-functional equation, optimal order of convergence, q-difference equation, uniqueness and regularity of solution

Publication Date

2011

Source Publication Title

IMA Journal of Numerical Analysis

Volume

31

Issue

2

Start Page

698

End Page

718

Publisher

Oxford University Press

ISSN (print)

02724979

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