二维抛物型方程的高精度分支稳定隐格式  

A High Accuracy Implicit Difference Scheme With Branching Stability for Solving Two-Dimension Parabolic Equation

作　　者：詹涌强[1] 杨小辉[2] 谭志明[3] 

机构地区：[1]华南理工大学广州学院计算机工程学院,广东广州510800 [2]广东警官学院计算机系,广东广州510440 [3]广东理工职业学院数学教研室,广东中山528458

出　　处：《安徽师范大学学报（自然科学版）》2015年第3期233-237,共5页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(61070165);广东省教育部产学研结合项目(2011B090400458)

摘　　要：用待定系数法构造了求解二维抛物型方程的高精度分支稳定隐式差分格式.格式的截断误差达到O(Δt2+Δx4).证明了当r≥1/6时,差分格式是稳定的.通过数值试验,比较了差分格式的解和精确解的区别,说明了差分格式的有效性.Proposed in the paper was an implicit difference scheme with high accuracy and branching stability for solving two-dimension parabolic equation by the method of undetermined parameters. The truncation error of the scheme was O（Δt^2＋Δx^4）.The difference scheme was proved to be stable if r≥1/6The numerical experiment showed the numerical solutions of difference scheme and the precise solutions were matched and the difference scheme was effective.

关 键 词：二维抛物型方程 隐式差分格式 截断误差 

分 类 号：O241.82[理学—计算数学]