Ordinary Differential Equations Numerical Solution Of The Time Behavior

In this paper, the long-time behavior of the numerical solutions to a class of initial value problems in ordinary differential equations is considered.Because of the complexity of this problem, the numerical approximation method which can't be applied to all kinds of solutions to the equations will achieve relative good conclutions when it is applied to the solution tending to the balance point .Euler method, single step method and one-leg multistep method are considered as maily numerical computation schemes. The long-time stability and convergence of numerical solutions is obtained and the con-clution that numerical solutions also can tend to the balance point is obtained as well.