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arXiv · 2601.18505

Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation

Chang Hou·Hu Chen·Jian Wang
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Abstract

In this paper, we discretize the Caputo time derivative of order \alpha \in (0,1) using the Alikhanov scheme on a quasi-graded temporal mesh, and employ the Newton linearization method to approximate the nonlinear term. This yields a linearized fully discrete scheme for the two-dimensional nonlinear time fractional subdiffusion equation with weakly singular solutions. For the purpose of conducting a pointwise convergence analysis using the comparison principle, we develop a new stability result. The global L^2-norm convergence order is min{\alpha r, 2}, and the local L^2-norm convergence order is min{r, 2} under appropriate conditions and assumptions. Ultimately, the rates of convergence demonstrated by the numerical experiments serve to validate the analytical outcomes.

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BibTeXRIS

Chang Hou, Hu Chen, Jian Wang. 2026-01-26. Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation. https://arxiv.org/abs/2601.18505

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