Bounds of high quality for first kind Volterra integral equations (Q1916972)

The author considers the linear Volterra integral equation of the first kind \[ \int^s_0 k(s,t) y(t) dt = g(s), \quad 0 \leq s \leq a\tag{*} \] which under some assumptions is equivalent to the Volterra integral equation of the second kind \[ y(s) = {g'(s)\over k(s,s)} - \int^s_0 {1\over k(s,s)} {\partial k(s,t) \over \partial s} y(t)dt, \quad 0 \leq s \leq a. \] Enclosure algorithms for linear Volterra integral equations of the second kind are derived. These methods are applied to several numerical examples of the form (*) and the results of the enclosure method and the discretization method are compared.