Delay-dependent Stability Analysis Of Numerical Methods For Neutral Delay Differential Equations

Neutral delay differential equations (NDDEs) arise in a wide variety of scientific and engi-neering applications, including circuit analysis, real-time simulation of mechanical (multibody)systems, chemical process simulation and optimal control. Because of the complexity of theNDDEs, it becomes quite difficult to obtain their analytic solution and hence it is necessary toinvestigate the numerical methods for solving NDDEs.There exists an extensive literature on numerical solution of NDDEs. A great deal of progresshas been made in the delay-independent stability analysis of the numerical methods for NDDEs.However, only few research works have been done on the delay-dependent stability of NDDEs.In this thesis, we first introduce a sufficient condition for the asymptotic stability of NDDEs.Based on this condition, we study the delay-dependent stability of linear multistep methods andnatural Runge-Kutta methods for NDDEs. Sufficient conditions for the numerical methods to bedelay-dependently stable are obtained and then used to give some examples of delay-dependentlystable linear multistep methods and natural Runge-Kutta methods for NDDEs. Several numericalexperiments are conducted to verify our theoretic results.