@Article{JCM-40-3,
author = {Xiaoli, Li and Yanping, Chen and Chuanjun, Chen},
title = {An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {3},
pages = {453--471},
abstract = {<p style="text-align: justify;">A combined scheme of the improved two-grid technique with the block-centered finite difference method is constructed and analyzed to solve the nonlinear time-fractional parabolic equation. This method is considered where the nonlinear problem is solved only on a coarse grid of size $H$ and two linear problems based on the coarse-grid solutions and one Newton iteration is considered on a fine grid of size $h$. We provide the rigorous error estimate, which demonstrates that our scheme converges with order $\mathcal{O}(\Delta t^{2-\alpha}+h^2+H^4)$ on non-uniform rectangular grid. This result indicates that the improved two-grid method can obtain asymptotically optimal approximation as long as the mesh sizes satisfy $h=\mathcal{O}(H^2).$ Finally, numerical tests confirm the theoretical results of the presented method.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2011-m2020-0124},
url = {https://global-sci.com/article/84186/an-improved-two-grid-technique-for-the-nonlinear-time-fractional-parabolic-equation-based-on-the-block-centered-finite-difference-method}
}