Discussion On Numerical Solutions And Stability Of Second-order Delay Differential Equations

This paper is concerned with the numerical and stability of solutions for several second-order delay differential equations, which is composed of four parts.In the first chapter, the research background and practical significance of the topics are simply summarized.The second chapter is concerned with the numerical solutions and stability of second-order delay differential equations. The sufficient and necessary condition is given under which the existence and uniqueness of periodic solutions is guaranteed. The numerical solutions and its stability are considered by using Newton method.In the third chapter, the analytical solutions and numerical solutions of second-order delay differential equation are considered by one-legθ-methods. A necessary and sufficient condition is given by analyzing eigenvalues of characteristic equation. It is proved that the numerical method is stable whenθ=1.The four chapter, we deal with the neutral equation as follow The eigenvalues of linear characteristic equation are analyzed in detail. The numerical solutions by one-legθ- methods are constructed and its stability is obtained. Specially, it is proved that the numerical method is stable whenθ=1.