The NGP-stability of Runge-Kutta methods for systems of neutral delay differential equations

Summary.

This paper deals with the stability analysis of implicit Runge-Kutta methods for the numerical solutions of the systems of neutral delay differential equations. We focus on the behavior of such methods with respect to the linear test equations \begin{eqnarray*} y'(t)&=& Ly(t)+My(t-\tau)+Ny'(t-\tau), \quad t\ge 0, y(t)&=& g(t), \quad -\tau\le t\le 0, \end{eqnarray*} where $\tau>0$,L, M and N are $d\times d$ complex matrices. We show that an implicit Runge-Kutta method is NGP-stable if and only if it is A-stable.