Superconvergence of collocation methods for a class of weakly singular Volterra integral equations

Authors:
Teresa Diogo;Pedro Lima
Affiliations:
Centro de Matemática e Aplicaçíes, Instituto Superior Técnico/UTL, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;Centro de Matemática e Aplicaçíes, Instituto Superior Técnico/UTL, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

We discuss the application of spline collocation methods to a certain class of weakly singular Volterra integral equations. It will be shown that, by a special choice of the collocation parameters, superconvergence properties can be obtained if the exact solution satisfies certain conditions. This is in contrast with the theory of collocation methods for Abel type equations. Several numerical examples are given which illustrate the theoretical results.