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
Liang, Hui, and Hermann Brunner. "Integral-algebraic equations: Theory of collocation methods I." SIAM Journal on Numerical Analysis 51.4 (2013): 2238-2259.