A fully discrete local discontinuous Galerkin method based on generalized numerical fluxes to variable-order time-fractional reaction-diffusion problem with the Caputo fractional derivative

Autor:	Lijie Liu, Xiaojing Wei, Leilei Wei
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	caputo fractional derivative generalized alternating numerical flux stability error estimate Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 9, Pp 5701-5715 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023289?viewType=HTML
Popis:	In this paper, an effective numerical method for solving the variable-order(VO) fractional reaction diffusion equation with the Caputo fractional derivative is constructed and analyzed. Based on the generalized alternating numerical flux, we get a fully discrete local discontinuous Galerkin scheme for the problem. From a practical standpoint, the generalized alternating numerical flux, which is distinct from the purely alternating numerical flux, has a more extensive scope. For $ 0 < \alpha(t) < 1 $, we prove that the method is unconditionally stable and the errors attain $ (k+1) $-th order of accuracy for piecewise $ P^k $ polynomials. Finally, some numerical experiments are performed to show the effectiveness and verify the accuracy of the method.
Databáze:	Directory of Open Access Journals
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