Stability Analysis Of Second Order Linear Delay Differential Equations

Second-order linear delay differential equations have been widely used in the fields of power system,control theory,pulse theory and so on.Most of the delay differential equations theoretical solution are difficult to obtain,and sometimes even impossible to find theoretical solution of the equation,so the numerical solution of the differential equations is particularly important.However,the stability of the numerical method is the first to consider,so the stability analysis of the equation is very necessary.In this paper,we mainly study the stability of the theoretical solutions and numerical solutions of the second-order delay linear differential equations.This paper is divided into two parts.The first chapter mainly introduces the research back ground of delay differential equations and its development situation at home and abroad.The second chapter studies the asymptotic stability of the theoretical solution of the second-order constant multi-delay differential equations,and accordings to the special properties of the quadratic equation,the second-order equation can be translated into first-order multi-delay systems,by the characteristic equation of the first-order multi-delay systems,a sufficient condition is given of the second-order equations.Then the one-leg ?- method is used to solve the model equations,and the conditions for the asymptotic stability of the numerical solution are given.