Abstract
We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.
Original language | English |
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Pages (from-to) | 899-920 |
Number of pages | 22 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 54 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2016 |
Scopus Subject Areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Auto-convolution volterra integral equations
- Collocation methods
- Existence and regularity of solutions
- Optimal order of convergence
- Superconvergence