Stability of the Radau IA and Lobatto IIIC methods for neutral delay differential system

Numerical stability is considered for several Runge–Kutta methods to systems of neutral delay differential equations. The linear stability analysis is adopted to the system. Adapted with the equistage interpolation process as well as the continuous extension, the Runge–Kutta methods are shown to have the numerical stability similar to the analytical asymptotic stability with arbitrary stepsize, when certain assumptions hold for the logarithmic matrix norm on the coefficient matrices of the NDDE system.