一种二阶常微分方程的数值解法  

A Numerical Method for Solving Second Order Ordinary Differential Equations

作　　者：户永清 陈正文 HU Yongqing;CHEN Zhengwen(Intelligent Manufacturing School of Sichuan University of Arts and Science,Dazhou Sichuan 635000,China;The Second Middle School of Bazhong City,Bazhong Sichuan 636000)

机构地区：[1]四川文理学院智能制造学院,四川达州635000 [2]巴中市第二中学,四川巴中636000

出　　处：《四川文理学院学报》2023年第5期39-44,共6页Sichuan University of Arts and Science Journal

基　　金：达州市智能制造产业技术研究院2022年度开放基金项目(ZNZZ2201)。

摘　　要：提出一种求二阶常微分方程数值解的规范,分三步进行,通过降阶,利用四阶龙格-库塔法、结合辛普森数值积分法迭代出原函数数值解.通过物理学上的三个具体的运动,建立二阶常微分方程,求其数值解并与解析解比较,发现用本文的数值解法与真实解符合的很好,具有较高的精度.In this paper,a specification for the numerical solution of the second order ordinary differential equation is presented.It is carried out in three steps.By reducing the order,the numerical solution of the original function is iterated by using the fourth order Runge-Kutta method and Simpson numerical integration method.The second order ordinary differential equation is established through three specific motions in physics,and its numerical solution is obtained and compared with the analytical solution.It is found that the numerical solution in this paper is in good agreement with the real solution and has high accuracy.

关 键 词：二阶常微分方程 数值解法 龙格—库塔法 泰勒展式 辛普森积分法 

分 类 号：O224[理学—运筹学与控制论]