求解一维非定常对流扩散反应方程的高精度紧致差分格式  

High Order Compact Difference Scheme for Solving the Unsteady Convection Diffusion Reaction Equation

作　　者：张亚刚[1] 马廷福[1] 王燕[1] 葛永斌[1] 

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《数学的实践与认识》2017年第13期263-270,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361045;11662016);宁夏高等学校科学技术研究项目(NGY2015023);宁夏大学研究生创新项目(GIP2017042)

摘　　要：提出了数值求解一维非定常对流扩散反应方程的一种高精度紧致隐式差分格式,其截断误差为O(τ~4+τ~2h^2+h^4),即格式整体具有四阶精度.差分方程在每一时间层上只用到了三个网格节点,所形成的代数方程组为三对角型,可采用追赶法进行求解,最后通过数值算例验证了格式的精确性和可靠性.A high-order compact finite difference implicit scheme is proposed for solving the one-dimensional unsteady convection diffusion reaction equation. The local truncation error of the scheme isO（τ^4 ＋ τ^2h^2 ＋ h^4）, The proposed scheme is overall fourth-order accuracy. The linear system arising from the scheme for the problem is tridiagonal. It can be solved by Thomas algorithm. Finally, numerical experiments are conducted to verify the accuracy and the reliability of the present scheme.

关 键 词：对流扩散反应方程 非定常 紧致差分格式 隐式格式 高精度 

分 类 号：O241.8[理学—计算数学]