两类基于MATLAB的非线性微分方程数值解的算法研究

The Algorithms About the Two Types of Numerical Solution of Nonlinear Differential Equations Based on MATLAB

通过对工程动态控制及计算机仿真中有重要应用的两类非线性微分方程数值解的数学算法分析,建立四阶定步长Runge-Kutta及Lorenz模型数值解的MATLAB算法结构,讨论了变步长情形下的误差控制,绘制了基于MATLAB的Lorenz系统数值解在二维和三维空间下的图形,提出了在可接受误差限内的数值解检验的基本思路.

Based on the mathematical algorithm analysis for the two kinds of nonlinear differential equation numerical solutions in engineering dynamic control and the important applications in computer simulation,the essay establishes a fourth-order fixed step length Runge-Kutta and the algorithm structure of Lorenz model numerical solution MATLAB,discusses the error control variable step size case, draws a numerical solution of the Lorenz system under the two-dimensional and three-dimensional graphics based on the MATLAB,and finally points out the numerical solution in testing the basic train of thought within acceptable error limits.