TY - JOUR
T1 - A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis
AU - Ma , Li
AU - Fu , Hongfei
AU - Zhang , Bingyin
AU - Xie , Shusen
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 429
EP - 462
PY - 2024
DA - 2024/05
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0108 
UR - https://global-sci.org/intro/article_detail/nmtma/23107.html
KW - Time-fractional reaction-diffusion equation, compact BCFD method, fast $L1$ method, $α$-robust unconditional stability, error estimates.
AB - <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>