@article{Chou2022, 
author = {Lot-Kei Chou and Siu-Long Lei},
title = {High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {4},
pages = {1463-1476},
keywords = {alternating direction implicit method, high dimension, advection-dispersion equations, Riesz fractional derivative, distributed-order, compression format},
url = {https://www.sciopen.com/article/10.3934/era.2022077},
doi = {10.3934/era.2022077},
abstract = {A second order alternating direction implicit scheme for time-dependent Riesz space distributed-order advection-dispersion equations is applied to higher dimensions with the Tensor-Train decomposition technique. The solutions are solved in compressed format, the Tensor-Train format, and the errors accumulated due to compressions are analyzed to ensure convergence. Problems with low-rank data are tested, the results illustrated a steeper growth in the ranks of the numerical solutions than that in related works.}
}