Yazar "Huntul, Mousa J." seçeneğine göre listele

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    An inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation
    (Hacettepe Univ, Fac Sci, 2023) Huntul, Mousa J.; Tekin, Ibrahim
    In this article, simultaneous identification of the time-dependent lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge of additional measurements is studied. Existence and uniqueness of the solution is proved by means of the contraction mapping on a small time interval. Since the governing equation is yet ill-posed (very slight errors in the time-average temperature input may cause relatively significant errors in the output potential and source terms), we need to regularize the solution. Therefore, regularization is needed for the retrieval of unknown terms. The 2D problem is discretized using the alternating direction explicit (ADE) method and reshaped as non-linear least squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Finally, we present a numerical example to demonstrate the accuracy and efficiency of the proposed method. Our numerical results show that the ADE is an efficient and unconditionally stable scheme for reconstructing the potential and source coefficients from minimal data which makes the solution of the inverse problem (IP) unique.
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    Öğe
    An Inverse Problem of Reconstructing the Unknown Coefficient in a Third Order Time Fractional Pseudoparabolic Equation
    (Univ Craiova, 2024) Huntul, Mousa J.; Tekin, Ibrahim; Iqbal, Muhammad K.; Abbas, Muhammad
    In this paper, we have considered the problem of reconstructing the time dependent potential term for the third order time fractional pseudoparabolic equation from an additional data at the left boundary of the space interval. This is very challenging and interesting inverse problem with many important applications in various fields of engineering, mechanics and physics. The existence of unique solution to the problem has been discussed by means of the contraction principle on a small time interval and the unique solvability theorem is proved. The stability results for the inverse problem have also been presented. However, since the governing equation is yet ill-posed (very slight errors in the additional input may cause relatively significant errors in the output potential), the regularization of the solution is needed. Therefore, to get a stable solution, a regularized objective function is to be minimized for retrieval of the unknown coefficient of the potential term. The proposed problem is discretized using the cubic B-spline (CB-spline) collocation technique and has been reshaped as a non-linear least-squares optimization of the Tikhonov regularization function. The stability analysis of the direct numerical scheme has also been presented. The MATLAB subroutine lsqnonlin tool has been used to expedite the numerical computations. Both perturbed data and analytical are inverted and the numerical outcomes for two benchmark test examples are reported and discussed.
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    Öğe
    On an inverse problem for a nonlinear third order in time partial differential equation
    (Elsevier B.V., 2022) Huntul, Mousa J.; Tekin, Ibrahim
    In this article, first we convert an inverse problem of determining the unknown timewise terms of nonlinear third order in time partial differential equation (PDE) from knowledge of two boundary measurements to the auxiliary system of integral equations. Then, existence and uniqueness of the solution of this system is proved by means of the contraction principle on a small time interval. Also uniqueness of the solution of the inverse problem is given. However, since the governing equation is yet ill-posed (very slight errors in the temperature input may cause relatively significant errors in the output potential and source terms), we need to regularize the solution. Therefore, to get a stable solution, a regularized cost function is to be minimized for retrieval of the unknown terms. The third order in time PDE problem is discretized using the FDM and reshaped as non-linear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Both analytical and perturbed data are inverted. Numerical outcomes for two benchmark test examples are reported and discussed. The proposed numerical approach has also been discussed. © 2022 The Author(s)