中文摘要：

许多物理现象中的稳定过程都归结为椭圆型微分方程,差分法是解椭圆型微分方程的重要方法.首先给出了解椭圆型微分方程五点差分格式的算法框架,然后对数学物理问题中的热传导方程及附加条件作差分逼近,求出其数值解,最后将理论应用于实际中去,在实践中得到可行性的检验.

英文摘要：

Many stable process in physical phenomena can be formulated as elliptic differential equations.Finite difference method is an important method to solve the elliptic differential equation.This paper first provides the algorithm framework of the five-point difference scheme of the elliptic equations,and then makes the finite difference approximation on heat conduction equation and additional in mathematical physics equations conditions,obtains its numerical solution.Finally,application of the theory is made and the practical feasibility test in practice is obtained.