Volterra-Type Integral Equations of the Second Kind With Nonsmooth Solutions: High-Order Methods Based on Collocation Techniques

Methods with arbitrary orders of convergence are derived for the approximate solution of second-kind Volterra integral equations with weakly singular kernels where exact solutions have unbounded derivatives at the left endpoint of the interval of integration. These methods are based on collocation techniques in certain nonsmooth piecewise function spaces whose elements reflect the singular behavior of the given equation. 9 refs.