Restoration of the merely time-dependent lowest term in a linear Bi-flux diffusion equation

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dc.authorid0000-0001-6725-5663
dc.contributor.authorAlosaimi, M.
dc.contributor.authorTekin, I.
dc.contributor.authorCetin, M. A.
dc.date.accessioned2026-01-24T12:31:02Z
dc.date.available2026-01-24T12:31:02Z
dc.date.issued2024
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThis paper investigates the inverse problem of determining the merely time-dependent lowest term and the particle concentration in a linear Bi-flux diffusion equation from knowledge of the particle concentration at the left boundary. The unique solvability of this inverse problem is established through the application of the contraction principle for sufficiently small time intervals. To solve this problem computationally, it is reformulated as a nonlinear least-squares minimization problem with simple bounds on the unknown coefficient, and to ensure stability the Tikhonov regularization is employed. The Crank-Nicolson finite-difference scheme is developed to solve the direct problem. On the other hand, the nonlinear least-squares minimization problem is iteratively solved using the built-in subroutine lsqnonlin from the MATLAB optimization toolbox. Numerical findings for two benchmark examples, involving the recovery of smooth and non-smooth time-dependent lowest terms, are presented and analyzed.
dc.description.sponsorshipTaif University; Deanship of Graduate Studies and Scientific Research, Taif University
dc.description.sponsorshipThe authors would like to acknowledge Deanship of Graduate Studies and Scientific Research, Taif University for funding this work.
dc.identifier.doi10.1007/s40314-024-02937-7
dc.identifier.issn2238-3603
dc.identifier.issn1807-0302
dc.identifier.issue8
dc.identifier.scopus2-s2.0-85204788179
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1007/s40314-024-02937-7
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5609
dc.identifier.volume43
dc.identifier.wosWOS:001318533200004
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Heidelberg
dc.relation.ispartofComputational & Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectInverse coefficient problem
dc.subjectBi-flux equation
dc.subjectFourier method
dc.subjectTikhonov regularization
dc.subjectNonlinear optimization
dc.titleRestoration of the merely time-dependent lowest term in a linear Bi-flux diffusion equation
dc.typeArticle

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