Department of Mathematics
Integral-algebraic equations: Theory of collocation methods I
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. © 2013 Society for Industrial and Applied Mathematics.
ν-smoothing Volterra operator, Collocation solutions, Index-μ tractability, Integral-algebraic equations, Optimal order of convergence, Tractability index
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Liang, Hui, and Hermann Brunner. "Integral-algebraic equations: Theory of collocation methods I." SIAM Journal on Numerical Analysis 51.4 (2013): 2238-2259.