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

• DOI: 10.1007/s002110050399
• Publication Date: 2002-08-25T07:47:25Z
• Authors: Lin Qiu; Biao Yang; Jiaoxun Kuang
• Keywords: Runge–Kutta methods; Delay differential equation

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 \(\) 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.