二维抛物型方程的一族高精度分支稳定显格式  

A FAMILY OF HIGH ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 2-D PARABOLIC EQUATION

作　　者：詹涌强 Zhan Yongqiang(Department of Mathematics Education,Guangdong Communication Polytechnic College,Guangzhou 510800)

机构地区：[1]广东交通职业技术学院基础部数学教研室,广州510800

出　　处：《高等学校计算数学学报》2021年第1期16-27,共12页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1 引言在渗流、扩散、热传导等领域中经常会遇到求解二维抛物型方程的初边值问题■(1)其中,φ,f1,f2,f3,f4为已知的光滑函数,a>0为热扩散项系数.对问题(1)的求解,有限差分法是解决此类问题的常用方法,常见的差分格式有古典显式格式与Crank-Nicolson格式[1-2],古典显式格式稳定性条件为r≤1/4,局部截断误差为O (Δt+Δx2).Proposed in the paper was an explicit difference scheme with high ac-curacy and branching stability for solving two-dimension parabolic type equation by the method of undetermined parameters.The truncation error of the scheme was O(△t^(3)+△x^(4)).The difference scheme was proved to be stable if r<1/2.The.numerical experiment shows the numerical solutions of difference scheme and the precise solutions are matched and the difference scheme is effective.

关 键 词：二维抛物方程 显式差分格式 截断误差 

分 类 号：O241.3[理学—计算数学]