27/03/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building
Arvet Pedas, Institute of Applied Mathematics, Tartu University, Estonia
High-order methods for Volterra integral equations with weak
singularities
We consider the numerical solution of some classes of linear
Volterra integral equations with singularities. We apply to them a
smoothing transformation so that the exact solution of the
resulting equation does not contain any singularities in its
derivatives up to a certain order. After that the regularized
equation is solved by a piecewise polynomial collocation method on
a mildly graded or uniform grid. Global convergence estimates are
derived and some superconvergence results are given.
