An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method |
| |
Authors: | Xiaoli Li Yanping Chen & Chuanjun Chen |
| |
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. |
| |
Keywords: | Improved two-grid Time-fractional parabolic equation Nonlinear Error estimates Numerical experiments. |
|
| 点击此处可从《计算数学(英文版)》浏览原始摘要信息 |