A formally second order BDF ADI difference scheme for the three-dimensional time-fractional heat equation
A formally second order BDF ADI difference scheme for the three-dimensional time-fractional heat equation
复制标题
三维时间分数热方程的形式二阶 BDF ADI 差分格式
DOI：
10.1080/00207160.2019.1607843
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发表时间：
2020-05
影响因子：
1.8
通讯作者：
Zhou Jun
中科院分区：
文献类型：
--
作者：
Chen Hongbin;Xu Da;Cao Jiliang;Zhou Jun
摘要 交替方向隐式（ADI）方法被广泛使用且计算效率高，可用于多维演化方程的数值逼近。本文主要制定并分析了三维时间分数热方程的形式二阶后向微分公式（BDF）ADI差分格式。时间导数采用二阶BDF方案近似，积分项采用二阶卷积求积处理。采用有限差分法进行空间离散，构造全离散格式。定义了两个新的内积和相应的范数来分析该方案。稳定性和收敛性是通过能量法推导出来的。报告了与我们的分析完全一致的数值实验。本方案与现有方案之间的比较表明，本算法比现有算法表现出更好的性能。
ABSTRACT Alternating direction implicit (ADI) method is widely utilized and computationally efficient for numerical approximation of the multidimensional evolution equations. This paper mainly formulates and analyzes a formally second order backward differentiation formula (BDF) ADI difference scheme for the three-dimensional time-fractional heat equation. The time derivative is approximated by second order BDF scheme and the integral term is treated by means of second order convolution quadrature. A fully discrete scheme is constructed with space discretization by finite difference method. Two new inner products and corresponding norms are defined to analyze the scheme. The stability and convergence are derived by the energy method. Numerical experiment in total agreement with our analysis is reported. Comparisons between the present schemes and the existing ones are included, showing that the present algorithms exhibit better performances than the existing ones.
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影响因子：
2.5
作者：
M. Khebchareon;A. K. Pani;G. Fairweather
通讯作者：
M. Khebchareon;A. K. Pani;G. Fairweather
二维分数阶演化方程的交替方向隐式欧拉法
影响因子：
4.1
作者：
Li, Limei;Da Xu
通讯作者：
Da Xu
DOI：
10.2307/3620819
发表时间：
2000-11
期刊：
The Mathematical Gazette
影响因子：
--
作者：
G. Leversha
通讯作者：
G. Leversha
影响因子：
3.9
作者：
Hongbin Chen;Da Xu;Jiliang Cao;Junjun Zhou
通讯作者：
Hongbin Chen;Da Xu;Jiliang Cao;Junjun Zhou
影响因子：
2.1
作者：
LUBICH, C
通讯作者：
LUBICH, C