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Author: search.filters.author.Sazaklıoğlu, Ali UğurHas files: No

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Now showing 1 - 6 of 6
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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.
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    Existence and Uniqueness Results for an Inverse Problem for Semilinear Parabolic Equations
    (UNIV NIS, FAC SCI MATH, 2017) Sazaklioglu, Ali Ugur; Ashyralyev, Allaberen; Erdogan, Abdullah Said; Sazaklıoğlu, Ali Uğur; Turkish Aeronautical Association; Turk Hava Kurumu University; Near East University; Institute of Mathematics & Mathematical Modeling; Peoples Friendship University of Russia; Kazakh British Technical University
    In the present study, unique solvability of an inverse problem governed by semilinear parabolic equations with an integral overdetermination is investigated. Furthermore, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.
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    Numerical solution of a source identification problem: Almost coercivity
    (WALTER DE GRUYTER GMBH, 2019) Ashyralyev, Allaberen; Erdogan, Abdullah Said; Sazaklioglu, Ali Ugur; Sazaklıoğlu, Ali Uğur; Near East University; Peoples Friendship University of Russia; Turk Hava Kurumu University; Turkish Aeronautical Association; Istanbul University
    The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.
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    Investigation of a Time-Dependent Source Identification Inverse Problem with Integral Overdetermination
    (TAYLOR & FRANCIS INC, 2017) Ashyralyev, Allaberen; Sazaklioglu, Ali Ugur; Sazaklıoğlu, Ali Uğur; Near East University; Peoples Friendship University of Russia; Institute of Mathematics & Mathematical Modeling; Turkish Aeronautical Association; Turk Hava Kurumu University
    In the present paper, a time-dependent source identification problem subject to an integral overdetermination is considered. Stability estimates for this differential problem are established. Furthermore, a first and a second order of accuracy difference schemes are proposed for the approximate solution of this problem. Stability and almost coercive stability estimates for these difference schemes are established. Additionally, some illustrative numerical results are provided.
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    On the unique solvability of an inverse problem for a semilinear equation with final overdetermination
    (AMER INST PHYSICS, 2016) Sazaklioglu, Ali Ugur; Erdogan, Abdullah Said; Ashyralyev, Allaberen; Sazaklıoğlu, Ali Uğur; Turkish Aeronautical Association; Turk Hava Kurumu University; Fatih University; Institute of Mathematics & Mathematical Modeling
    This paper deals with existence and uniqueness of the solution of an inverse problem for a semilinear equation subject to a final overdetermination in a Banach space. Moreover, the first order of accuracy Rothe difference scheme is presented for the numerical solution of this problem. The existence and uniqueness result for this difference scheme is given. This difference scheme is applied on a particular example and some numerical results are given.