二维抛物型方程的分支稳定显式差分格式  

An explicit difference scheme with branching stability for solving parabolic equation of two-dimension

作　　者：詹涌强[1] 陈妙玲[1] 谭志明[2] 

机构地区：[1]华南理工大学广州学院数学教研室,广东广州510800 [2]广东理工职业学院数学教研室,广东中山528458

出　　处：《暨南大学学报（自然科学与医学版）》2013年第5期467-470,共4页Journal of Jinan University(Natural Science & Medicine Edition)

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的显式差分格式.格式的截断误差达到O(Δt2+Δx4).证明了当1/12≤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.An explicit difference scheme with high accuracy and branching stability for solving two-di- mension parabolic type equation was proposed by the method of undetermined parameters. The truncation error of the scheme was O（△t2＋△x^4）.The difference scheme was proved to be stable if12^-1≤r≤6-1.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：二维抛物型方程 显式差分格式 截断误差 

分 类 号：O241.82[理学—计算数学]