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Research Article | Open Access

High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format

Lot-Kei Chou, Siu-Long Lei( )
Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
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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.

Keywords

high dimensionadvection-dispersion equationsRiesz fractional derivativedistributed-orderalternating direction implicit methodcompression format

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Electronic Research Archive
Volume 30 Issue 4,
April 2022
Pages 1463-1476
DOI: 10.3934/era.2022077

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Cite this article:
Chou L-K, Lei S-L. High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format. Electronic Research Archive, 2022, 30(4): 1463-1476. https://doi.org/10.3934/era.2022077

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Received: 30 December 2021
Revised: 15 February 2022
Accepted: 13 March 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)