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An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method

An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method
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Year:    2022

Author:    Xiaoli Li, Yanping Chen, Chuanjun Chen

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 453–471

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2011-m2020-0124

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 453–471

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Improved two-grid Time-fractional parabolic equation Nonlinear Error estimates Numerical experiments.

Author Details

Xiaoli Li

Yanping Chen

Chuanjun Chen

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