The complexity of solving the traditional second order differential equation is high. In order to simplify the process of solving second order differential equations, a new growth analysis method for numerical solutions of second order differential equations is designed based on improved genetic algorithm. On the basis of the improved genetic algorithm, the value of the second order differential equation in the vicinity of Julia direction is analyzed by analyzing the definition and notation of the second order differential equation, and then the growth of the numerical solution of the second order differential equation is analyzed by combining the convex hull and the remainder terms of the second order differential equation, thus simplifying the solving process of the second order differential equation. The experiment finds that the numerical solution accuracy of the second order differential equation is improved effectively by the growth analysis process.