基于MATLAB一阶微分方程的仿真  

Simulation of First Order Differential Equation Based on MATLAB

作　　者：任春年 李会荣 魏倩茹 REN Chunnian;LI Huirong;WEI Qianru(School of Mathematics and Computer Application,Shangluo University,Shangluo 726000,China)

机构地区：[1]商洛学院数学与计算机应用学院,陕西商洛726000

出　　处：《现代信息科技》2021年第15期160-162,共3页Modern Information Technology

基　　金：2020年商洛市科技计划项目(2020-Z-0043);2018年商洛学院科研基金项目(18SKY009);2019年商洛学院校级应用数学科研创新团队(19SCX02)。

摘　　要：为得到更加精确的求解微分方程数值解的方法,采用了显式欧拉法、隐式欧拉法、改进欧拉法以及四阶龙格库塔等方法与MATLAB软件中专有的ode45函数作比较,对用不同方法来求解微分方程的求解结果进行了研究,通过例证以及数据分析,得出在步长h任意时,四阶龙格库塔法的精准度、稳定性都要高于其他三种欧拉法,使在微分方程求解方法的选择上更具针对性。In order to obtain a more accurate numerical solution of differential equations,the explicit Euler method,implicit Euler method,improved Euler method and fourth-order Runge-Kutta method are compared with the special ode45 function of MATLAB software.The results of solving differential equations by different methods are studied.Through examples and data analysis,when the step h is arbitrary,the accuracy and stability of the fourth-order Runge-Kutta method are higher than the other three Euler methods,which makes the choice of differential equation solution method more targeted.

关 键 词：微分方程 欧拉法 四阶龙格库塔法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]