1、 常微分方程的求解问题 摘 要 题目中显然涉及到求解数值积分和求解常微分方程问题. 首先，需要对常微分方程中的数值积分进行求解.回顾所学过的求解数值积分的方 法，有Newton-Cotes公式、复化求积公式、Romberg算法和Gauss-Legender公式等，我们 选择其中的一种方法来进行求解.在求解时， 选择了包含在Newton-Cotes公式中的梯形公 式进行了求解. 然后，将积分求解的结果代入原方程中，进一步再求解常微分方程.回顾所学过的 求解常微分方程的方法，有Euler格式、后退的Euler格式、梯形格式、改进的Euler格式、 Euler两步格式、Runge-Kutta 方法、
2、Taylor级数法等，我们选择其中的一种方法进行求 解.在求解时，选择了四阶 Runge-Kutta 方法进行了求解. 最后，应用 MATLAB 软件进行了求解计算了 t=1,2,10 时的值，并对模型进行了 优缺点分析及模型的推广. 关键词：数值积分；常微分方程；Newton-Cotes 公式；Runge-Kutta 方法； MATLAB 软件 THE SOLUTION OF ORDINRY DIFFERENTIAL EQUATIONS ABSTRACT Problems in apparently involves numerical integration and solving pro
3、blems in ordinary differential equations. First of all, we need to give the solution of ordinary differential equations. Take a review of the numerical integration method, a Newton-Cotes formula, complex formula, Romberg algorithm and Gauss-Legender formula, we choose one of the methods to solve the
4、 problem. In this method, we choose the Newton-Cotes formula which includes the trapezoid formula to get the solution. Then, the integral solution should be used in the original equation, and then get the solution of ordinary differential equation. Take a review of what has been learned for solving ordinary differential equation method, are Euler format, Euler format, the format back trapezoid, improved Euler format, Euler two, Runge-Kutta method, Taylor format series method, we choose one of t
