TY - JOUR
T1 - Discrete superconvergence of collocation solutions for first-kind volterra integral equations
AU - Liang, Hui
AU - BRUNNER, Hermann
N1 - The first author’s research is supported by the National Nature Science Foundation of China (No. 11101130), the Heilongjiang University Science Funds for Young Scholar (No. QL201004) and the Research Fund of the Heilongjiang Provincial Education Department (No. 12511414). She gratefully acknowledges the financial support and the hospitality extended to her by HKBU’s Department of Mathematics. The work of the second author was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406) and by the Hong Kong Research Grants Council (RGC Grant HKBU 200207).
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Collocation solutions
KW - First-kind volterra integral equations
KW - Piecewise polynomials
KW - Superconvergence at non-mesh points
UR - http://www.scopus.com/inward/record.url?scp=84872483187&partnerID=8YFLogxK
U2 - 10.1216/JIE-2012-24-3-359
DO - 10.1216/JIE-2012-24-3-359
M3 - Journal article
AN - SCOPUS:84872483187
SN - 0897-3962
VL - 24
SP - 359
EP - 391
JO - Journal of Integral Equations and Applications
JF - Journal of Integral Equations and Applications
IS - 3
ER -