On Galerkin methods for Abel-type integral equations

Galerkin methods are studied for the numerical solution of Abel-type integral equations. In order to maintain the causality/triangularity of the resulting system of linear equations, spline functions of maximal defect are used, i.e., $C^{ - 1} $ piecewise polynomials. Asymptotically optimal error estimates in the supremum norm are proved. Both robustness and accuracy of the Galerkin methods are compared with those of collocation methods. Some numerical experiments using some “cheap” quadrature schemes that work quite well under certain circumstances only are shown, and some generally applicable quadrature methods are reported.