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Author: search.filters.author.Sazaklıoğlu, Ali UğurStart date: 2022

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    On the numerical solutions of some identification problems for one- and multidimensional parabolic equations backward in time
    (ELSEVIER, 2022) Sazaklioglu, Ali Ugur; Sazaklıoğlu, Ali Uğur; Turk Hava Kurumu University; Turkish Aeronautical Association
    In this paper, an abstract (differential) inverse problem backward in time, that is a class of some identification problems for simultaneous determination of the source and initial condition, is considered. A finite difference scheme is constructed for the numerical solution of this abstract problem. Some stability and almost coercive stability estimates for the constructed difference scheme are established by the tools of operator theory. Furthermore, the proposed abstract difference scheme and the acquired results for that are extended for several applications involving identification problems for one-and multidimensional parabolic equations. Finally, sundry illustrative numerical results and visualizations are carried out and discussed.(c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
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    An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation
    (ELSEVIER, 2024) Sazaklioglu, Ali Ugur; Sazaklıoğlu, Ali Uğur; Turkish Aeronautical Association; Turk Hava Kurumu University
    The main aims of this paper are to investigate the existence and uniqueness results for the solution of an inverse source problem for a multidimensional, semilinear, backward parabolic equation, subject to Dirichlet boundary conditions, and to propose an iterative difference scheme for the numerical solution of the problem. The unique solvability of the difference scheme is established, as well. In the foundation of the theoretical results, some tools and facts from the operator theory, contraction principle and the Banach fixed-point theorem are applied. Furthermore, a comprehensive numerical analysis and several illuminating visualizations are carried out by employing the iterative difference schemes proposed on some test problems.