GP(G)-stability of Runge-Kutta methods for generalized delay differential systems
The GP(G)-stability of Runge-Kutta methods for the numerical solutions of the systems of delay differential equations is considered. The stability behaviour of implicit Runge-Kutta methods (IRK) is analyzed for the solution of the system of linear test equations with multiple delay terms. After an establishment of a sufficient condition for asymptotic stability of the solutions of the system, a criterion of numerical stability of IRK with the Lagrange interpolation process is given for any stepsize of the method. (C) 1999 Elsevier Science Ltd. All rights reserved.
gp(g)-stability runge-kutta method generalized delay differential system