 Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous mediaYuxuan Niu, Yang Liu, Hong Li and Fawang Liu Mathematics and Computers in Simulation (MATCOM), 2023, vol. 203, issue C, 387-407 Abstract: In this article, we present an efficient numerical algorithm, which combines the fourth-order compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ method, to solve the nonlinear distributed-order fractional Sobolev model appearing in porous media. We also construct the corrected CDS by adding the starting part to deal with the problem with nonsmooth solution and recovery the convergence rate. We derive optimal convergence results and prove the stability of the presented numerical algorithm. Finally, we implement numerical experiments by taking several examples with smooth and nonsmooth solutions to verify the correctness of the theoretical results, the effectiveness of the corrected algorithm and the computational efficiency of the fast algorithm. Keywords: FBN-θ method; Fast TT-M algorithm; Compact difference scheme; Nonlinear distributed-order fractional Sobolev equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:203:y:2023:i:c:p:387-407 DOI: 10.1016/j.matcom.2022.07.001 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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