Department of Mathematics
Discrete superconvergence of collocation solutions for first-kind volterra integral equations
It is known that collocation solutions for firstkind Volterra integral equations based on (discontinuous or continuous) piecewise polynomials cannot exhibit local superconvergence at the points of a uniform mesh. In this paper we present a complete analysis of local superconvergence of such collocation solutions for first-kind Volterra integral equations at non-mesh points. In particular, we discuss (i) the existence of superconvergence points for prescribed collocation points; (ii) the existence of collocation points for prescribed superconvergence points. Numerous examples illustrate the theory. © 2012 Rocky Mountain Mathematics Consortium.
Collocation solutions, First-kind volterra integral equations, Piecewise polynomials, Superconvergence at non-mesh points
Source Publication Title
Journal of Integral Equations and Applications
Rocky Mountain Mathematics Conso
Link to Publisher's Edition
Liang, Hui, and Hermann Brunner. "Discrete superconvergence of collocation solutions for first-kind volterra integral equations." Journal of Integral Equations and Applications 24.3 (2012): 359-391.