@article{856d4e8138034ce1b0d878bdfe34b65c,
title = "The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations",
abstract = "Collocation solutions by globally continuous piecewise polynomials to second-kind Volterra integral equations (VIEs) with smooth kernels are uniformly convergent only for certain sets of collocation points. In this paper we establish the analogous convergence theory for VIEs with weakly singular kernels, for both uniform and graded meshes.",
keywords = "Collocation solutions, Globally continuous piecewise polynomials, Uniform convergence, Volterra integral equations, Weakly singular kernels",
author = "Hui Liang and Hermann Brunner",
note = "Funding Information: The work of the first author was supported by the National Natural Science Foundation of China grants 11771128 and 11101130, by the China Scholarship Council grant 201708230219, and by the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province grant UNPYSCT-2016020. The work of the second author was supported by the Hong Kong Research Grants Council GRF grants HKBU 200113 and 12300014. Publisher copyright: {\textcopyright} 2019, Society for Industrial and Applied Mathematics",
year = "2019",
month = jul,
day = "30",
doi = "10.1137/19M1245062",
language = "English",
volume = "57",
pages = "1875--1896",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "4",
}