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

Carrer, J.A.M.; Solheid, B.S.; Trevelyan, J.; Seaid, M.

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.

Citation

Carrer, J., Solheid, B., Trevelyan, J., & 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, 132-144. https://doi.org/10.1016/j.enganabound.2020.10.017

• Journal Article Type: Article
• Acceptance Date: Oct 22, 2020
• Online Publication Date: Oct 30, 2020
• Publication Date: 2021-01
• Deposit Date: Nov 5, 2020
• Publicly Available Date: Oct 30, 2021
• Journal: Engineering Analysis with Boundary Elements
• Print ISSN: 0955-7997
• Electronic ISSN: 1873-197X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 122
• Pages: 132-144
• DOI: https://doi.org/10.1016/j.enganabound.2020.10.017
• Public URL: https://durham-repository.worktribe.com/output/1287237