五点差分格式算法在数学物理方程中的应用  

Applications of five point difference format algorithm to elliptic equations

作　　者：林爽[1] 张杰[2] 姜行健[3] 

机构地区：[1]大连工业大学信息科学与工程学院,辽宁大连116034 [2]辽宁师范大学数学学院,辽宁大连116029 [3]大连理工大学机械工程与材料能源学部,辽宁大连116024

出　　处：《辽宁师范大学学报（自然科学版）》2012年第4期467-470,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11071029)

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.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.

关 键 词：椭圆方程 五点差分格式 热传导方程 

分 类 号：O241.82[理学—计算数学]