%0 Journal Article
%T 求解对流扩散方程的一种高精度紧致差分格式<br>A High-Order Compact Difference Scheme for Solving Convection-Diffusion Equations
%A 罗传胜
%A 李春光
%A 董建强
%A 景何仿&lt
%A br&gt
%A LUO Chuan-sheng
%A LI Chun-guang
%A DONG Jian-qiang
%A JING He-fang
%J 西南大学学报(自然科学版)
%D 2018
%R 10.13718/j.cnki.xdzk.2018.09.014
%X 在指数变换的基础上，将对流扩散方程变为扩散方程，消除了数值求解中较难处理的对流项，采用四阶紧致差分方法离散扩散方程的空间变量，采用扩展的<inline-formula>$\frac{1}{3} $</inline-formula>
		-Simpson公式离散时间变量，格式的截断误差为<i>O</i>（<i>τ</i><sup>4</sup>+<i>h</i><sup>4</sup>）.理论分析证明该格式是无条件稳定的.通过数值算例验证了本文方法的有效性.<br>In this paper, based on exponential transform, the convection diffusion equation is transformed into a diffusion equation, thus eradicating the advection term, which is hard to treat in numerical solution. A high-order accurate implicit compact difference scheme is constructed for solving the one dimensional parabolic equation by the fourth-order pade' formula combined with time extension of the <inline-formula>$\frac{1}{3} $</inline-formula>-Simpson formulas. The truncation error of the scheme is <i>O</i>(<i>τ</i><sup>4</sup>+<i>h</i><sup>4</sup>). A theoretical analysis shows that the scheme is unconditionally stable. Numerical experiments verify the accuracy and reliability of the present scheme
%K 高精度紧致格式
%K 无条件稳定
%K 指数变换
%K 数值计算
%K 扩展的$\frac{1}{3} $-Simpson公式&lt
%K br&gt
%K high-order compact scheme
%K unconditionally stable
%K exponential transformation
%K numerical calculation
%K extension of the $\frac{1}{3} $-Simpson
%U http://xbgjxt.swu.edu.cn/jsuns/html/jsuns/2018/9/20180914.htm