Cauchy微分方程的一种新的数值解法

A NEW NUMERICAL SOLUTION OF CAUCHYDIFFERENTIAL EQUATION

众所周知，求解微分方程（组）常用的数值方法有有限差分法，有限元素法等，这些方法都是将微分方程（组）分离散化后求解．若将网格划分得粗了，则求解精度不高，不能满足工程实际需要，若将网格划分得细了，则所需计算机内存量和计算量都太大．为解决上述问题，本文给出微分方程（组）的解的概率表达式的一种新的数值解法──概率数值解法．

It is common knowledge that the numerical solution of differential equationsgenerally have the method of limited difference and the method of limited element, et alAfter the differential equations to be divided, the solution will be obtained by these methods. If the net is divided roughly, the precision is not high and can't meet the real engineering requirements. If the net is divided minutely, the required store volume inside computer and the amount of counting are very large. To solve these problems, this paper givea new numerical solution of the probability expression on the solution of differential equa tions, numerical solution of probability.