On the stability of Runge-Kutta methods for delay intergral equations

We present a class of Runge-Kutta methods for the numerical solution of a class of delay integral equations (DIEs) described by two different kernels and with a fixed delay τ. The stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters. The results are then applied to collocation methods. In particular we obtain that any collocation method for DIEs, resulting from an A-stable collocation method for ODEs, with a stepsize which is submultiple of the delay τ, preserves the asymptotic stability properties of the analytic solutions