TY - JOUR
T1 - Integral-Algebraic Equations
T2 - Theory of Collocation Methods I
AU - Liang, Hui
AU - Brunner, Hermann
N1 - Funding information:
School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang, China ([email protected]). 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’s Republic of China ([email protected]), an d Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’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:
© 2013, Society for Industrial and Applied Mathematics
PY - 2013/8/1
Y1 - 2013/8/1
N2 - 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.
AB - 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.
KW - ν-smoothing Volterra operator
KW - Collocation solutions
KW - Index-μ tractability
KW - Integral-algebraic equations
KW - Optimal order of convergence
KW - Tractability index
UR - http://www.scopus.com/inward/record.url?scp=84888870458&partnerID=8YFLogxK
U2 - 10.1137/120894567
DO - 10.1137/120894567
M3 - Journal article
AN - SCOPUS:84888870458
SN - 0036-1429
VL - 51
SP - 2238
EP - 2259
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 4
ER -