Numerical method for fractional sub-diffusion equation with space–time varying diffusivity and smooth solution
Using a new generalized L2 formula and a time varying compact finite difference operator, we construct a high order numerical scheme for a class of generalized fractional diffusion equation with space–time varying diffusivity that admits a smooth solution. The convergence order is shown to be O(τz3−...
Zapisane w:
| Główni autorzy: | , |
|---|---|
| Format: | Статья |
| Język: | English |
| Wydane: |
Elsevier B.V.
2025
|
| Hasła przedmiotowe: | |
| Dostęp online: | https://dspace.ncfu.ru/handle/123456789/29619 |
| Etykiety: |
Dodaj etykietę
Nie ma etykietki, Dołącz pierwszą etykiete!
|
| Streszczenie: | Using a new generalized L2 formula and a time varying compact finite difference operator, we construct a high order numerical scheme for a class of generalized fractional diffusion equation with space–time varying diffusivity that admits a smooth solution. The convergence order is shown to be O(τz3−α+h4) via the energy method and demonstrated by numerical experiments. Our contributions, which improve some previous work, focus primarily on two aspects: (i) we develop a novel generalized L2 formula achieving O(τz3−α) accuracy; (ii) we derive an essential a priori estimate for a time-varying compact finite difference operator, ensuring the new numerical scheme is stable and convergent. |
|---|