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.
出处
《郑州大学学报（理学版）》
CAS
北大核心
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)
关键词
扩散方程
PADÉ逼近
紧致格式
广义梯形公式
稳定性
diffusion equation
Padé approximation
compact scheme
generalized trapezoidal formula
stability
