title: Stability of Runge-Kutta methods for delay integro-differential equations
abstract: We study stability of Runge-Kutta (RK) methods for delay integro-differential equations with a constant delay on the basis of the linear equation du/dt = Lu(t) + Mu(t- tau ) + K integral /sub t- tau //sup t/ u( theta )d theta , where L, M, K are constant complex matrices. In particular, we show that the same result as in the case K = 0 (Koto, 1994) holds for this test equation, i.e., every A-stable RK method preserves the delay-independent stability of the exact solution whenever a step-size of the form h = tau /m is used, where m is a positive integer
keyphrases: stability Runge-Kutta methods delay integro-differential equations constant delay