单步法求解常微分方程初值问题  

Solution of Initial Value in Ordinary Differential Equation via Single-step Method

作　　者：张秋生[1] 

机构地区：[1]新乡职业技术学院,河南新乡453006

出　　处：《科技通报》2012年第2期7-9,共3页Bulletin of Science and Technology

摘　　要：在科学和工程技术实例应用中,有许多数学模型是以常微分方程的形式建立起来的。因此,常微分方程求解问题是一个在科学计算中占有相当重要地位的问题。由常微分方程的理论可以看到,虽然许多常微分方程的解是存在的,但是却并不能用简单的初等函数来表现出来,甚至有的不能给出解的具体表达形式。因此,对于常微分方程初值问题的数值解法的研究是非常必要的。本文主要介绍了两种单步法,即欧拉法和改进的欧拉法来求解常微分方程初值问题,并通过具体的数值算例来进行比较,表明改进的欧拉法具有一定的优势。There are many mathematical models are based on the form of Ordinary Differential Equation in the application of science and engineering. The problem of how to solve Ordinary Differential Equation has a important position scientific calculation. From the theory of Ordinary Differential Equation, we can see, although many ordinary differential equations do have solutions, but they can＇t be performed in simple elementary function, even some of them can＇t be expressed with specific solution. For this reason, it is very necessary for us to study the numerical methods of Ordinary Differential Equation. This article mainly introduced two kinds of single step processes to solve the problems of the Ordinary Differential Equation initial value, that＇s Euler method and the improved Euler method. Through the concrete numerical example, we compare the two methods, obviously the improved Euler method has an absolute advantage.

关 键 词：常微分方程 数值解法 初值问题 欧拉法 改进的欧拉法 

分 类 号：O1[理学—数学]