求解对流扩散方程的一种高精度紧致差分格式  

A High-Order Compact Difference Scheme for Solving Convection-Diffusion Equations

作　　者：罗传胜 李春光 董建强 景何仿[3] LUO Chuan-sheng;DONG Jian-qiang;LI Chun-guang;JING He-fang(School of Mathematics and Information Science,Beifang University of Nationalities,Yinchuan 750021,China;School of Civil Engineering,Beifang University of Nationalities,Yinchuan 750021,China;Institute of Numerical Calculation and Engineering Application,Beifang University of Nationalities,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]北方民族大学土木工程学院,银川750021 [3]北方民族大学数值计算与工程应用研究所,银川750021

出　　处：《西南大学学报（自然科学版）》2018年第9期91-95,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11361002;11761005)

摘　　要：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1/3-Simpson公式离散时间变量,格式的截断误差为O(τ~4+h^4).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.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 1/3-Simpson formulas.The truncation error of the scheme is O（τ~4＋h^4）.A theoretical analysis shows that the scheme is unconditionally stable.Numerical experiments verify the accuracy and reliability of the present scheme.

关 键 词：高精度紧致格式 无条件稳定 指数变换 数值计算 扩展的1/3-Simpson公式 

分 类 号：O241.82[理学—计算数学]