Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels

In this paper we investigate the attainable order of (global)convergence of collocation approximations in certain polynomialspline spaces for solution of Volterra integrodifferential equationswith weakly singular kernels. While the use of quasi-uniformmeshes leads, due to the nonsmooth nature of these solutions,to convergence of order less than one, regardless of the degreeof the approximating spline function, collocation on suitablygraded meshes will be shown to yield optimal convergence rates.