Stability Analysis Of Generalized Neutral Delay Differential Systems

Delay differential equations(DDEs) plays a very significant role in a wide variety, for ex-ample Physics, Engineering, Biology, Medical Science, Economic fields and so on. Its stabilityof theoretical solution and numerical solutions have drawn attention of many scholars, and havemany results by now. Meanwhile, neutral delay differential equations(N DDEs) is special sub-class of DDEs,which are arised from various fields of applied sciences, for example, the cellproliferation model is N DDEs.Recently, there are many results of the stability of numerical methods for N DDEs. How-ever, there are few researches about numerical stability of generalized neutral delay differentialequations(GN DDEs) and the conditions of L-stable. Therefore, it is significant to study theL-stability. This paper will study the stability of GN DDEs.Firstly, it has simply introduced the thesis research situation and some basic knowledge ofdelay differential equations. Secondly, given the conditions of N GP GL-stability of theoreticalsolution, discussed the stability of the block θ-method for the numerical solution of the systems ofGN DDEs, and it is proved that the block θ-method is N GP G-stability and N GP GL-stabilityconditions, respectively θ∈[12,1] and θ=1. At last, it discussed the N GP GL-stability ofRunge-Kutta methods for the numerical solution of GN DDEs, and it is proved that L-stabilityRunge-Kutta methods can preserve the stability of the underlying systems.