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.
Original language | English |
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Pages (from-to) | 698-718 |
Number of pages | 21 |
Journal | IMA Journal of Numerical Analysis |
Volume | 31 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2011 |
Scopus Subject Areas
- General Mathematics
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- collocation solutions
- functional equation with vanishing delay
- integro-functional equation
- optimal order of convergence
- q-difference equation
- uniqueness and regularity of solution