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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.