求解二维扩散方程的一种高精度紧致差分格式  

A High-order Compact Difference Scheme for Solving the Two-dimensional Diffusion Equation

作　　者：尹治丹 陈建华[1] 葛永斌[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《四川师范大学学报（自然科学版）》2015年第3期365-370,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11361045和11161036)资助项目

摘　　要：扩散方程通常用来描述扩散现象中的物质密度的变化或者与扩散相类似的现象,针对二维扩散方程提出了一种高精度紧致差分格式,该格式基于四次样条函数对空间变量进行离散,对时间导数采用(2,2)Padé逼近,从而得到了时间和空间均为四阶精度的紧致差分格式.然后证明了该格式是无条件稳定的.最后通过数值实验,验证方法的精确性和稳定性.The diffusion equations are usually used to describe the change of density of substance in diffusion or the similar phenomenon.In this paper,a high-order compact difference scheme is proposed for solving the two-dimensional diffusion equation.The quartic spline function is used for the spatial discretization and the （2,2） Padé approximation method is used for the temporal discretization.The scheme is fourth order accuracy in both time and space.Then,it is proved that this scheme is unconditionally stable.At last,numerical experiments are carried out to demonstrate its accuracy and stability.

关 键 词：扩散方程 四次样条函数 PADÉ逼近 高精度紧致格式 无条件稳定 

分 类 号：O241.82[理学—计算数学]