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.
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Received February 10, 1997 / Revised version received January 5, 1998
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Qiu, L., Yang, B. & Kuang, J. The NGP-stability of Runge-Kutta methods for systems of neutral delay differential equations. Numer. Math. 81, 451–459 (1999). https://doi.org/10.1007/s002110050399
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DOI: https://doi.org/10.1007/s002110050399