Title: A mollified approach to reconstruct an unknown boundary condition for the heat conduction equation of fractional order

Authors: Afshin Babaei; Seddigheh Banihashemi

Addresses: Department of Applied Mathematics, University of Mazandaran, Babolsar, 47416-95447, Iran ' Department of Applied Mathematics, University of Mazandaran, Babolsar, 47416-95447, Iran

Abstract: We consider an inverse problem of time fractional heat conduction problem. It is shown that the problem is ill-posed. A method is investigated based on the finite difference to find heat distribution and boundary values. The discrete mollification regularisation is applied to obtain a stable numerical solution. Finally, some test problems are investigated to show the ability of the proposed scheme.

Keywords: heat conduction equation; Caputo's derivative; ill-posedness; mollification; finite difference.

DOI: 10.1504/IJCSM.2021.120685

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.4, pp.369 - 379

Accepted: 11 Jun 2020
Published online: 03 Feb 2022 *

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