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 本文針對(duì)一階線性常微分方程初值問題的連續(xù)有限元法的超收斂性和穩(wěn)定性作了分析,并對(duì)一階線性常微分方程初值問題的具有4階精度的三類數(shù)值方法??經(jīng)典runge-kutta法(單步法),adams隱式格式(多步法),連續(xù)有限元法的穩(wěn)定性作了比較。