沃尔什级数求解线性偏微分方程和积分方程的新方法

本文提出了用沃尔什级数求解高阶线性偏微分方程的一种新方法。先将偏微分方程化成积分方程,再用逐步逼近法来确定方程的沃尔什级数形式的近似解。本方法的特点是:①可以确定较高阶微分方程的近似解,②沃尔什函数具有取值的简单性,从而简化了计算的编程工作。本文先将偏微分方程化成积分方程,讨论了解的存在唯一性,提出对偏微分方程求解的方法,最后给出了实例。

To Solve Partial Differential and Integral Equation With Walsh Series

This paper proposes a new method of solving the high order linear partial differential equation by means of Walsh Series. With this method, the discussed partial differential equation should be first changed into an integral equation,and then by using succesive appro- ximation, the approximate solution in the form of Walsh Series will be found. The new method has the following characteristics: (1) it can be used to find the approximate solution of high order differ- ential equation; (2) because it is computer-oriented, Walsh function could facilitate image and signal processing. So this method is inv- olved in computer. What we have done is that we have changed the partial differential equation in this paper into integral equation, di- scussed the existance and uniqueness of its solution, proposed method and procedure in solving the partial differential equation, and final- ly given some computation exampls as well.