@article{c4b70032725f47d299b32150e2e8bfaa,
title = "Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations",
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.",
keywords = "Auto-convolution volterra integral equations, Collocation methods, Existence and regularity of solutions, Optimal order of convergence, Superconvergence",
author = "Ran Zhang and Hui Liang and Hermann Brunner",
note = "Funding information: The research of the authors was supported by the NSF of China (11101130, 11271157, U1530116, 11471141, 11371171), the Program for New Century Excellent Talents in University of Ministry of Education of China, the Research Fund of the Heilongjiang Provincial Education Department for the Academ ic Backbone of the Excellent Young People (1254G044), the Heilongjiang University Science Funds for Distinguished Young Scholars (JCL201303), the Natural Science Foundation of Heilongjiang Province (A201211), the Hong Kong Research Grants Council (HKBU 200211), and the Natural Scien ces and Engineering Research Council of Canada (NSERC Discovery Grant 9406). Publisher copyright: {\textcopyright} 2016, Society for Industrial and Applied Mathematics",
year = "2016",
month = mar,
day = "29",
doi = "10.1137/15M1019362",
language = "English",
volume = "54",
pages = "899--920",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "2",
}