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

Journal of Computational and Applied Mathematics, 218 (2008), 307-316
http://dx.doi.org/10.1016/j.cam.2007.01.023

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.