Stability Analysis Of Multistep Runge-kutta Methods For Several Classes Of Multidelay Differential Equations

Delay differential equations are widespread and we often use them in medicine,chemistry, mechanical engineering, electronic communications engineering,population growth, management system and many other domains. In addition, delay differential equations can consider the impact of the history of system on current situation effectively. Because of these characteristics, the study of them is very meaningful. However, for many delay differential equations, the analytical solutions are not easy to obtain, people are gradually interested in the numerical solutions.In the past several decades, predecessors have studied the delay differential equations using linear multistep methods, ?-methods, Runge-Kutta methods, and have achieved much. In addition, numerical stability is quite an important portion of numerical analysis. So in this paper, we consider to use multistep Runge-Kutta methods to study the numerical stability of delay differential equations.In this paper, we study the numerical stability of multistep Runge-Kutta methods for three classes of the multidelay differential equations. They are respectively neutral fixed-length delay differential algebraic equation, neutral multidelay differential algebraic equation and multidelay integro-differential equations. For this three classes of multidelay differential equations, the asymptotic stability of theory solutions have been discussed by scholars. And on this basis, in this paper we use the multistep Runge-Kutta methods for the further research and deduce the sufficient conditions for its stability under the condition of asymptotic stability of equation themselves. In the end, numerical experiments are carried to verify the conclusions.