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A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem.

Carrer, J.A.M. and Solheid, B.S. and Trevelyan, J. and Seaid, M. (2021) 'A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem.', Engineering analysis with boundary elements., 122 . pp. 132-144.

Abstract

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted Residuals Method approach with the steady state fundamental solution for anisotropic media playing the role of the weighting function, one obtains the boundary integral equation of the proposed formulation. The presence of a domain integral with the fractional time derivative as part of its integrand, and the evaluation of this fractional time derivative as a Caputo derivative, constitute the main feature of the formulation. The analyses of some examples, in which the numerical results are always compared with the corresponding analytical solutions, show the robustness of the formulation, as accurate results are obtained even for small values of the order of the time derivative.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.enganabound.2020.10.017
Publisher statement:© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:22 October 2020
Date deposited:10 November 2020
Date of first online publication:30 October 2020
Date first made open access:30 October 2021

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