Runge-Kutta methods for Volterra integral equations of the second kind

Some Runge-Kutta methods for the numerical solution of Volterra integral equations of the second kind have been considered previously, and these methods can be generalized in a natural way. By considering a class of variable-step quadrature methods, the Runge-Kutta methods appear as extensions of the step-by-step quadrature methods, and theoretical insight is readily obtained. Such insight may provide confidence limits when constructing practical algorithms.