matlab在常微分方程数值解中的应用

MATLAB 在常微分方程数值解中的应用摘 要】许多现实问题都可以通过微分方程的形式进行表示，传统解微分方程的方法有近似分析解法 、表解法和图解法,这些方法需对其进行大量的假设，而使得数学模型有一定的失真，有一定的局限性。数值解法利用计算机，使得求解更精确、效率更高，而 MATLAB 是一种数学软件包，有高级编程格式，使得计算结果更具有可信性,因此微分方程的求解及 MATLAB 在其中的应用具有实际意义。本文对常微分方程数值解问题作进一步探讨,并应用 MATLAB 对其中难解的改进 Euler 法和 Runge-Kutta 法进行编程实现，程序简洁、直观，求解速度快、方法有用性较强.【关 键 词】常微分方程 数值解 MATLAB Euler 法 龙格—库塔方法 ode45 ode15sMatlab in ordinary differential equation numerical solution of applicationYang Hua Zhang Lei【 Abstract 】 Many practical problems can be using differential equations in the form of representation ， the traditional method of solving differential equations are similar analysis method， table method and graphical method ， these methods to carry on the large amounts of hypothesis， so that the mathematical model has certain distortion, have certain limitation. Numerical solution of using a computer ， make solving more accurate and more efficient， and MATLAB is a kind of mathematics software package， with advanced programming format, making calculation result is more credibility, therefore differential equation and solution of the MATLAB in one of the application of practical significance. This paper numerical solution of differential equation problem further discussion， and the application of MATLAB in which the difficult solution improvement Euler method and Runge - Kutta method on the programming, the program is concise, intuitive and solution speed, method of practical stronger。【Key words】ordinary differential equation，numerical solution，Matlab，Euler method,Runge-Kutta method...