Year: 2023
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 353–370
Abstract
The aim of this paper is to study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This interesting model employs a nonlocal operator to replace the conventional first-order time-derivative. It introduces a finite memory effect of a constant length encoded through a kernel function. The nonlocal-in-time operator is related to fractional time derivatives that rely on the entire time-history on one hand, while reduces to, on the other hand, the classical time derivative if the length of the memory window diminishes. This allows us to demonstrate the effectiveness of the nonlocal-in-time model in capturing the crossover widely observed in nature between the initial sub-diffusion and the long time normal diffusion.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1014
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 353–370
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlocal model nonlocal operators mean square displacement sub-diffusion numerical methods.
Author Details
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Analysis and numerical methods for nonlocal‐in‐time Allen‐Cahn equation
Li, Hongwei
Yang, Jiang
Zhang, Wei
Numerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 6
https://doi.org/10.1002/num.23124 [Citations: 0]