求解常微分方程边值问题的差分方法

A Difference Method for Solution to Boundary Value Problem of Ordinary Differential Equations

差分法是求解常微分方程数值解的最重要方法之一。本文对差分法的基本思想作了简要的阐述,并利用差分法求解了常微分方程的边值问题,给出了边界条件的两种处理方法。实例证明用改进的方法求得的数值解具有较高的精度。

Difference method is one of the most important methods for numerical solution to ordinary differential equations. This paper makes a brief description on the basic idea of the differential method,and uses it to solve the boundary value problem of ordinary differential equations. Two methods are given for dealing with the boundary conditions. The examples prove that the numerical solutions by the improved method have a high accuracy.