This paper deals with the stability analysis of implicit Runge-Kutta methods for the numerical solutions of systems of generalized neutral delay differential equations. The stability behaviour of implicit Runge-Kutta ...This paper deals with the stability analysis of implicit Runge-Kutta methods for the numerical solutions of systems of generalized neutral delay differential equations. The stability behaviour of implicit Runge-Kutta methods is analysed for the solution of the generalized system of linear neutral test equations. After an establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, we show that a implicit Runge-Kutta method is NGPG-stable if and only if it is A-stable under some Lagrange interpolation condition.展开更多
文摘This paper deals with the stability analysis of implicit Runge-Kutta methods for the numerical solutions of systems of generalized neutral delay differential equations. The stability behaviour of implicit Runge-Kutta methods is analysed for the solution of the generalized system of linear neutral test equations. After an establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, we show that a implicit Runge-Kutta method is NGPG-stable if and only if it is A-stable under some Lagrange interpolation condition.
