@article{78ded2b34fe343cb98017b3a89e47278,

title = "Integral-Algebraic Equations: Theory of Collocation Methods I",

abstract = "Our analysis of collocation solutions for general systems of linear integral-algebraic equations (IAEs) is based on the notions of the tractability index and the ν-smoothing property of a Volterra integral operator. These are used to decouple the given IAE system into the inherent system of regular second-kind Volterra integral equations (VIEs) and a system of first-kind VIEs. This decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions. Numerical examples illustrate the theoretical results.",

keywords = "ν-smoothing Volterra operator, Collocation solutions, Index-μ tractability, Integral-algebraic equations, Optimal order of convergence, Tractability index",

author = "Hui Liang and Hermann Brunner",

note = "Funding information: School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang, China (wise2peak@126.com). This author was supported by the National Nature Science Foundation of China (11101130), the Research Fund of the Heilongjiang Provincial Education Department (12511414), and the Heilongjiang University Science Funds for Young Scholar (QL201004). *Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, People{\textquoteright}s Republic of China (hbrunner@math.hkbu.edu.hk), an d Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John{\textquoteright}s, A1C 5S7 NL, Canada. This author was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery grant 9406) and by the Hong Kong Research Grants Council (GRF grant 200207). Publisher copyright: {\textcopyright} 2013, Society for Industrial and Applied Mathematics",

year = "2013",

month = aug,

day = "1",

doi = "10.1137/120894567",

language = "English",

volume = "51",

pages = "2238--2259",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "4",

}