@article{Liu2023, 
author = {Lijie Liu and Xiaojing Wei and Leilei Wei},
title = {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},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {9},
pages = {5701-5715},
keywords = {Caputo fractional derivative, generalized alternating numerical flux, stability, error estimate},
url = {https://www.sciopen.com/article/10.3934/era.2023289},
doi = {10.3934/era.2023289},
abstract = {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  <  α  (  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.}
}