Computing guaranteed error bounds for problems in renewal theory

Abstract

Equations of renewal type are linear Volterra integral equations having the special form

$$x\left( s \right) = g\left( s \right) + \int_0^s {k\left( {s - t} \right)x\left( t \right)} dt,0 \leqslant s \leqslant a,a \in \left( {0,\infty } \right),$$

((1))

where the kernel and inhomogeneity are continuous. We are searching solutions in the real Banach Space B = C[0,a] which has the usual maximum norm.