Stability and pointwise-in-time convergence analysis of a finite difference scheme for a 2D nonlinear multi-term subdiffusion equation
In this paper, we aim to study the stability and convergence of a finite difference scheme for solving the two-dimensional nonlinear multi-term time fractional subdiffusion equation with weakly singular solutions. We apply the L1 scheme to discretize the multi-term temporal Caputo derivatives, a sta...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2025069 |
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| Summary: | In this paper, we aim to study the stability and convergence of a finite difference scheme for solving the two-dimensional nonlinear multi-term time fractional subdiffusion equation with weakly singular solutions. We apply the L1 scheme to discretize the multi-term temporal Caputo derivatives, a standard central difference method in space, and a backward formula to approximate the nonlinear term on the uniform mesh, respectively. Stability and pointwise-in-time error estimates are obtained for the fully discrete scheme. The global convergence order is $ \alpha_1 $, and the local convergence order is 1 in the temporal direction. The theoretical analysis is verified by some numerical results. |
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| ISSN: | 2688-1594 |