An efficient high‐order two‐level explicit/implicit numerical scheme for two‐dimensional time fractional mobile/immobile advection‐dispersion model

This article constructs a new two‐level explicit/implicit numerical scheme in an approximate solution for the two‐dimensional time fractional mobile/immobile advection‐dispersion problem. The stability and error estimates of the proposed technique are deeply analyzed in the L∞(0,T;L2)$$ {L}^{\infty}...

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Veröffentlicht in:International journal for numerical methods in fluids 2024-08, Vol.96 (8), p.1305-1336
1. Verfasser: Ngondiep, Eric
Format: Artikel
Sprache:eng
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Zusammenfassung:This article constructs a new two‐level explicit/implicit numerical scheme in an approximate solution for the two‐dimensional time fractional mobile/immobile advection‐dispersion problem. The stability and error estimates of the proposed technique are deeply analyzed in the L∞(0,T;L2)$$ {L}^{\infty}\left(0,T;{L}^2\right) $$‐norm. The developed approach is less time consuming, fourth‐order in space and temporal accurate of order O(k2−λ2)$$ O\left({k}^{2-\frac{\lambda }{2}}\right) $$, where k$$ k $$ is the time step and λ$$ \lambda $$ denotes a positive parameter less than 1. This result shows that the two‐level explicit/implicit formulation is faster and more efficient than a large class of numerical schemes widely discussed in the literature for the considered problem. Numerical experiments are performed to verify the theoretical studies and to demonstrate the efficiency of the new numerical method. Both figures and tables provide the stability analysis and convergence rate of the method. The approach is more efficient and effective (stable, second‐order convergent in time and fourth‐order spatial accurate) than a broad range of methods widely studied in literature for the considered problem. It can be considered as robust tools for integration of multidimensional problems.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.5296