@Article{NMTMA-17-429,
author = {Ma , LiFu , HongfeiZhang , Bingyin and Xie , Shusen},
title = {A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {2},
pages = {429--462},
abstract = {<p style="text-align: justify;">In this article, an $α$-th $(0 &lt; α &lt; 1)$ order time-fractional reaction-diffusion
equation with variably diffusion coefficient and initial weak singularity is considered. Combined with the fast $L1$ time-stepping method on graded temporal meshes,
we develop and analyze a fourth-order compact block-centered finite difference
(BCFD) method. By utilizing the discrete complementary convolution kernels and
the $α$-robust fractional Grönwall inequality, we rigorously prove the $α$-robust unconditional stability of the developed fourth-order compact BCFD method whether
for positive or negative reaction terms. Optimal sharp error estimates for both the
primal variable and its flux are simultaneously derived and carefully analyzed. Finally, numerical examples are given to validate the efficiency and accuracy of the
developed method.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0108 },
url = {http://global-sci.org/intro/article_detail/nmtma/23107.html}
}