求解Poisson方程Dirichlet问题的一点补充

A Supplement of Solving the Dirichlet Problems in Poisson Equations

求解Poisson方程定解问题通常有分离变量法、积分变换法、格林函数法等重要方法,但传统的求解方法有时运算量较大,求解较麻烦.通过寻求一类特殊的Poisson方程的Dirichlet问题求解方法,即-Δu=f(x)中的f(x)为多项式函数时,Poisson方程的Dirichlet问题可采用比较简单的求解方法,避免了传统求解方法的复杂计算,从而将求解Poisson方程定解问题的方法进一步完善.

Method of separation variables,the integral transform method and the Green function method were used to find fixed solutions of Poisson equations.But the traditional methods usually have complicated calculation and cannot easily help us to find the solutions.The paper tried a special method to solve the Dirichlet problems of Poisson equations.In the equation-Δu=f(x),some simpler methods can be used to solve the Dirichlet problems of Poisson equations when f(x)is a polynomial function.The methods can avoid complicated calculation and improve the methods for finding fixed solutions to problems of Poisson equations.