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−...
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| Автори: | , |
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| Формат: | Статья |
| Мова: | English |
| Опубліковано: |
Elsevier B.V.
2025
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| Предмети: | |
| Онлайн доступ: | https://dspace.ncfu.ru/handle/123456789/29619 |
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| Резюме: | 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. |
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