Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915756209340416 |
|---|---|
| author | Hou, Chang Chen, Hu Wang, Jian |
| author_facet | Hou, Chang Chen, Hu Wang, Jian |
| contents | In this paper, we discretize the Caputo time derivative of order α\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{αr, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation Hou, Chang Chen, Hu Wang, Jian Numerical Analysis In this paper, we discretize the Caputo time derivative of order α\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{αr, 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. |
| title | Pointwise-in-time convergence analysis of an Alikhanov scheme for a 2D nonlinear subdiffusion equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.18505 |