求解偏微分方程及方程组的一种新型分离变量法

求解偏微分方程及方程组时,通常采用的经典分离变量法和加法分离变量法增多存在一定的局限性,对于某些特定的方程类型需要有特殊的方法去解决.对于一类强非线性篇微分方程及方程组,提出一种新的分离变量法.该方法不但解决了此类方程的求解问题,而且还含有若干个任意函数,实际上解出了无穷多组解,对应无穷多个定解条件,针对不同的实际问题有不同的实际意义,对偏微分方程数值解的研究有一定的意义.

A New Variate-separating Method for Solving Partial Differential Equation System

The variate-separating method and adding variate-separating method usually used in solving partial differential equation systems have some limit and some special equation systems need special method. In this paper, a new variate-separating method is proposed for solving a special kind of strong non-linear partial differential equations. This method, while solving the special equation systems, has some arbitrary functions, and thus gives out infinite possible solutions that correspond to infinite boundary conditions. These solutions have different meanings for different actual problems. This metod plays some parts in the study of numerical solution of partial differential equation systems.