A recursive algorithm for the approximate solution of Volterra integral equations of the first kind of convolution type

In this paper we present an algorithm for the approximate solution of a class of Volterra integral equations of the first kind whose kernel depends on the difference of the arguments, i.e. a deconvolution algorithm. As is well known, this is an ill posed problem, but we give conditions under which the algorithm is robust against noise and sampling of the output. The class of systems for which we can prove consistency of the algorithm includes Abel equations with square integrable unknown input functions.