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Finite element method for a generalized constant delay diffusion equation

delete2024-07-01
delete2
PRE
AI
W
Weiping Bu
S
Sizhu Guan
徐
徐晓虹 (Xiaohong Xu)
Y
Yifa Tang *
DOI：10.1016/j.cnsns.2024.108015delete
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摘要

摘要

En 中文
本文考虑有限元方法求解广义常延迟扩散方程。研究了所考虑模型的解的规律性，与Tan等人 (2022) 相比，这是首次发现该解在时间上具有非均匀多奇异性。为了克服多奇异性，基于Caputo分数阶导数的L1公式和riemann-liouville分数阶积分的分数阶梯形公式，使用对称梯度网格为所考虑的问题设计了完全离散的有限元方案。然后我们研究了该方案的无条件稳定性。接下来，详细分析了L1公式和分数阶梯形公式的局部截断误差，特别是首次讨论了后者，在解的多奇异性和对称分级网格下。应用这些误差成果，我们获得了所提出的数值格式的收敛性。最后，通过数值试验验证了理论结果。
Keyword:
Fractional constant delay diffusion equation
Multi-singularity
Finite element method
Stability and convergence

期刊

Communications in Nonlinear Science and Numerical Simulation 封面图
Communications in Nonlinear Science and Numerical Simulation
IF:
3.8
论文数:
9.3K
被引数:
1.8W

机构

X
xiangtan university
学者数:
1.5W
论文数: 9.2K
被引数: 8
C
chinese academy of sciences
学者数:
56.7W
论文数: 45.0W
被引数: 704
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