Department of Mathematics
Analysis of collocation solutions for a class of functional equations with vanishing delays
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.
collocation solutions, functional equation with vanishing delay, integro-functional equation, optimal order of convergence, q-difference equation, uniqueness and regularity of solution
Source Publication Title
IMA Journal of Numerical Analysis
Oxford University Press
Brunner, Hermann, Hehu Xie, and Ran Zhang. "Analysis of collocation solutions for a class of functional equations with vanishing delays." IMA Journal of Numerical Analysis 31.2 (2011): 698-718.