Stability analysis of Runge–Kutta methods for systems of delay differential equations

This paper is concerned with the numerical solution of initial value problems for systems of delay differential equations. We consider adaptation of the class of Runge–Kutta methods, and investigate the stability of the numerical processes by considering their behaviour in the case of U′(t) = LU(t) + MU(t − τ) (t ≥ 0), where L, M denote constant complex matrices, that are not necessarily simultaneously diagonalizable, and τ>0.