Abstract
We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function θ(t) vanishing at the initial point of the given interval [0, T] (with θ(t) = qt, 0 > q > 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results.
Original language | English |
---|---|
Pages (from-to) | 3303-3332 |
Number of pages | 30 |
Journal | SIAM Journal of Scientific Computing |
Volume | 33 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2011 |
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Collocation solutions
- Existence and regularity of solutions
- Optimal order of convergence
- Pantograph-type delays
- Vanishing delays
- Volterra functional integral equations