Numerical Methods For Two Classes Of Delay Differential Equations

As an important branch of differential equations,delay differential equations have been widely used in many fields such as control and ecology.Because of the existence of timedelay terms,their analytical solutions are difficult to obtain,so solving numerical solutions becomes an important research direction.This thesis aims to study the numerical calculation methods of delay pseudo-parabolic differential equations and delay differential equations of neutral type.The main contents of this thesis are as follows:In the first part,this thesis studies the method of lines of delay pseudo-parabolic differential equation.Firstly,the method of lines is used to transform the delay pseudo-parabolic differential equation into delay differential algebraic equations,then the convergence analysis and error estimation are given.Furthermore,Runge-Kutta method is applied to the delay differential algebraic equation.Finally,numerical examples are given to illustrate the effectiveness of the theoretical results.In the second part,this thesis studies Rosenbrock method for delay differential equations of neutral type.Under the condition of delay-dependent stability of neutral delay differential equations,the weak time-delay correlation stability of Rosenbrock method for neutral delay differential equations is presented.Based on the argument principle,a sufficient condition of the weak delay asymptotic stability for Rosenbrock method is given.Finally,numerical examples are given to illustrate the effectiveness of the theoretical results.