Delay-Dependent Stability Of Multistep Runge-Kutta Methods For Delay Differential Systems Of Neutral Type

Delay differential equation is a class of functional differential equation.Since the delay differential equation belongs to an infinite dimensional system,it is hard to obtain the analytical solutions essentially.Therefore,it is necessary to study numerical solutions of delay differential equations.In this thesis,Delay-dependent stability of numerical methods for delay differential systems of neutral type is considered.Based on the Argument Principle,a sufficent condi-tion of weak delay-dependent stability of multistep Runge-Kutta methods for the systems is given.Futhermore,numerical examples are given to illustrate the effectiveness of the main results.The main contents are as follows:In the first chapter,this thesis introduces the research background and the research s-tatus of stability of numerical methods for delay differential equations.Some basic symbols are introduced.In the second chapter,a necessary and sufficient condition for the asymptotic stability of analytical solutions of linear neutral differential systems is described.Then,a relaxed definition for delay-dependent stability of numerical methods is presented.In the last chapter,the weak delay-dependent stability of multistep Runge-Kutta meth-ods is studied.Several conditions are obtained in terms of the argument principle.Further-more,an algorithm is given to check weak delay-dependent stability conditions.Finally,numerical examples are given to illustrate the effectiveness of the main results.