Stability analysis of runge-kutta methods for delay integro-differential equations

Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable RungeKutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.