The Solution of Volterra Integral Equations of the Convolution Type Using Two-point Rational Approximants

This paper applies the method of Laplace transform inversion using two-point rational approximants, introduced by Grundy (1977), to the solution of Volterra integral equations of the convolution type. The transforms which occur in solving these equations using Laplace transform methods are, in many cases, of the type which can be inverted by the method introduced in Grundy (1977). There are however additional difficulties which have to be met. Examples are given to illustrate their resolution and at the same time indicate the scope of the method. 1