求解扩散方程的一种高精度隐式差分方法  

High-order implicit difference method for the diffusion equation

作　　者：葛永斌[1] 田振夫[1] 詹咏[2] 吴文权[2] 

机构地区：[1]宁夏大学数学计算机学院,银川750021 [2]上海理工大学城市建设与环境工程学院,上海200093

出　　处：《上海理工大学学报》2005年第2期107-110,119,共5页Journal of University of Shanghai For Science and Technology

基　　金：教育部"高等学校优秀青年教师教学科研奖励计划"资助项目(2001年度);上海市教委青年基金资助项目(03GQ18);宁夏高等学校科学技术研究项目

摘　　要：利用一阶微商和二阶微商的四阶紧致差分逼近公式,推导出了数值求解一维扩散方程的两种新的高精度隐式紧致差分格式,其截断误差分别为O(τ2+h4)和O(τ4+h4).通过Fourier分析方法证明了格式O(τ2+h4)是无条件稳定的,而格式O(τ4+h4)是无条件不稳定的.并且由于每一时间层上只用到了3个网格点,所以差分方程可采用追赶法直接进行求解.Based on the fourth-order compact difference formulas for the first and second derivatives, two classes of new implicit difference schemes are proposed for solving the one-dimensional diffusion equation. The methods are of order O(τ2 + h4) and O (τ4 + h4) respectively. The former is proved to be unconditionally stable while the later is unconditionally unstable by Fourier analysis. The difference equation can be solved by the method of forward elimination and backward substitution. Numerical results show the efficiency and dependability.

关 键 词：扩散方程 紧致隐格式 高精度 差分方法 

分 类 号：O241.82[理学—计算数学]