Stability analysis of Runge-Kutta methods for Volterra integro-differential equations

Abstract This paper is concerned with the stability properties of Runge-Kutta methods for Volterra integro-differential equations. Both the basic test equation and a convolution test equation are considered. Some fixed order recurrence relations and the corresponding stability conditions are derived for general methods. The concept of V 0 -stability is introduced for the convolution test equation and some V 0 -stable one-stage methods are found. The A 0 -stability and V 0 -stability of the fully implicit discretized collocation methods with one or two stages are investigated in details. Finally, some numerical experiments are given to illustrate the obtained theoretical results.