Collocation Methods for Weakly Singular Second Kind Volterra Integral Equations with Nonsmooth Solution

摘要

The solution is approximated near zero by a linear combination of powers of the square root of t, and away from zero by the usual polynominal representation. Convergence is proved and many numerical experiments are presented with examples from the literature. A method of Brunner et al, originally developed for this kind of equation with a smooth solution, is compared for the numerical approximation of the moment integrals which emerge in the collocation scheme.