Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of theâ€¦ (More)

We discuss a possibility to construct high-order numerical algorithms on uniform or mildly graded grids for solving linear Volterra integral equations of the second kind with weakly singular or otherâ€¦ (More)

A discrete method of accuracy O(hm) is constructed and justi ed for a class of Fredholm integral equations of the second kind with kernels that may have weak diagonal and boundary singularities. Theâ€¦ (More)

For the Fredholm integral equation u=T u+f on the real line, fast solvers are designed on the basis of a discretized wavelet Galerkin method with the Sloan improvement of the Galerkin solution. Theâ€¦ (More)

On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem withâ€¦ (More)

We consider the generalized airfoil equation in the situation where the index of the problem is âˆ’1. We periodize the problem, then discretize it by a fully discrete version of the trigonometricâ€¦ (More)