本次课程设计中，主要讨论了常微分方程的初值问题数值解法。文章主要分3大块，分别是：1.简单介绍几种常微分方程的初值问题数值解的求法，给出其算法流程图和相应matlab程序。2.通过运用典型的数值解法如Eulor方法，改进Eulor方法，Runge-Kutta方法求解具体常微分方程并分析对比方法收敛阶、稳定性。3.进一步去用以上三种方法求解Lotka-Volterra方程，分析食饵与捕食者模型，得出相关结论。-The curriculum design, focused on the numerical solution of initial value problem of ordinary differential equations. This article mainly divided into three large pieces, namely: 1. brief introduction of several ordinary differential equation initial value problem of numerical solution method for finding, given its flow chart and the corresponding algorithm matlab program. 2. The method Eulor improve Eulor method, Runge-Kutta method to solve through the use of typical numerical solution of ordinary differential equations and specific analysis and comparison Convergence order and stability. 3. Further to the above three methods used to solve the Lotka-Volterra equations of prey and predator model, draw relevant conclusions.