Stochastic ordinary differential equation (SODE) is the product of the combination of probability theory and ordinary differential equation (ODE). It is more difficult to solve the exact solutions for stochastic differential equations than to solve the exact solutions of deterministic differential equations. In view of a popular interdisciplinary subject——sovliving stochastic differential equations, the application and comparison of the numerical solutions of stochastic differential equations are discussed in this paper. So we discussed numerical methods of stochastic differential equations, including Euler-Maruyama method, Milstein method and Runge-Kutta method. The differences between the exact solutions of stochastic differential equations and the exact solutions of deterministic differential equations under the influence of different Brownian motion are compared by several examples, and the results of different numerical methods and the errors between the numerical solutions and the exact solutions are also compared. The results show that the numerical solutions of the Milstein method and Runge-Kutta method are closer to the true solution than the Euler-Maruyama method, which are consistent with the theoretical analysis.This conclusion has some guiding significance for the theoretical methods and applications of numerical solutions of stochastic ordinary differential equations.