Computing The Characteristic Roots Of Neutral Delay Differential Equations

The NDDEs are used in many fields, but there are no so many papers had introduced them, so in this paper, you can learn some methods computing the characteristic roots of neutral delay-differential equationsThis paper consists of four chapters, in order to introduce the methods of computing the characteristic roots of neutral delay-differential equations.In the part of remind the past and now of the neutral delay- differential equations, it first shows the appliance of neutral delay-differential equations, recalls the developments of neutral delay-differential equations, and gives some applied models.In the second chapter, you can learn how to change the neutral delay-differential equations into an abstract Cauchy problem, and how to computing the characteristic roots using backward-difference-method. In the end this chapter verifies the stability of this method.In the third chapter, you can learn using RK -methods to compute the characteristic roots of neutral delay differential equations, and it also verifies the convergence of these methods.At last , this paper introduces a method of computing the convergence order of these methods, and it gives the convergence order of the two methods, so you can compare them and choose which one to use, in the end, it gives some figures of the characteristic roots computed by the two methods.