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2025, Volume 33, Issue 3: 1476-1489. doi: 10.3934/era.2025069
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Stability and pointwise-in-time convergence analysis of a finite difference scheme for a 2D nonlinear multi-term subdiffusion equation

  • School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
  • Received: 22 December 2024 Revised: 16 February 2025 Accepted: 27 February 2025 Published: 17 March 2025

  • 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.

    Citation: Chang Hou, Hu Chen. Stability and pointwise-in-time convergence analysis of a finite difference scheme for a 2D nonlinear multi-term subdiffusion equation[J]. Electronic Research Archive, 2025, 33(3): 1476-1489. doi: 10.3934/era.2025069

    Related Papers:

  • 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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