the aim of this thesis is to analyze the super-convergence and stability of continuous finite element methods which is a type of numerical me-thods solving the 1-degree lineal initial value problem of ordinary differential equation, and compare the stability of the three 4-order pre-cision numerical methods of the 1-degree initial value problem of ordinary differential equation-classical runge-kutta method ( single step method ), adams hidden method ( multiple step method ), and continuous finite element method 本文针对一阶线性常微分方程初值问题的连续有限元法的超收敛性和稳定性作了分析,并对一阶线性常微分方程初值问题的具有4阶精度的三类数值方法??经典runge-kutta法(单步法),adams隐式格式(多步法),连续有限元法的稳定性作了比较。