求解一维扩散方程的一种高精度紧致差分方法  

A High-order Compact Difference Method for the One-dimensional Diffusion Equation

作　　者：杨晓佳[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：《郑州大学学报（理学版）》2016年第1期10-16,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11361045;11161036);宁夏高等学校科学技术研究项目(NGY2013019)

摘　　要：针对一维扩散方程,空间采用四阶Padé公式,时间采用广义的梯形公式,差分离散得到了一种时间二阶、空间四阶精度的隐式紧致差分格式,其截断误差为O(τ2+h4).通过理论分析证明了此格式是无条件稳定的.最后通过数值实验验证了格式的精确性和可靠性.For the one dimensional diffusion equation,a high-order compact difference scheme was constructed by using the fourth-order Padé formula for space discretization and the generalized trapezoidal formula for time discretization,and the truncation error of the scheme was O（ τ2＋ h4）. The unconditional stability of the scheme was analyzed by theoritical method. Numerical experiments were carried out to verify the accuracy and the reliability of the present method.

关 键 词：扩散方程 PADÉ逼近 紧致格式 广义梯形公式 稳定性 

分 类 号：O241.82[理学—计算数学]