传统的二阶微分方程求解过程存在复杂度较高的问题。为了简化二阶微分方程的求解过程，基于改进遗传算法设计了一种新的二阶微分方程数值解增长性分析方法。在改进遗传算法的基础上，通过分析二阶微分方程的定义与记号，研究二阶微分方程在Julia方向附近的取值情况，然后结合二阶微分方程的凸包和余项，分析二阶微分方程数值解的增长性，从而简化了二阶微分方程的求解过程。实验表明：通过上述增长性分析过程，有效提高了二阶微分方程数值解的精度。

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.