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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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Bibliografiska uppgifter
Huvudupphovsmän: Alikhanov, A. A., Алиханов, А. А.
Materialtyp: Статья
Språk:English
Publicerad: Elsevier B.V. 2025
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Länkar:https://dspace.ncfu.ru/handle/123456789/29619
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Sammanfattning: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.