A fast and simple numerical method for a class of integral equations that generalizes the renewal-type equations: Z(t)=z(t) + \int_0^t f(y, Z(t-y)) dG(y). The method can also be used for solving renewal equations and estimating the renewal function. Such equations arise often also in the branching process theory and can be found in Galton-Watson, Bellman-Harris, Sevastyanov and Crump-Mode-Jagers branching processes, cancer growth models and more. Examples are included!