Volume 9, Issue 4 (12-2023)
mmr 2023, 9(4): 225-239 |
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University of Science and Technology of Mazandaran , k.rashedi@mazust.ac.ir
Abstract: (364 Views)
In this article, a linear inverse problem for approximating the right hand side of a fourth order parabolic equation is studied. In this problem, it is assumed that the homogeneous boundary conditions along with an integral condition on the time domain and a local condition at a point of the space domain are known. In the first step, we show that this problem has a unique classical solution. Then, we convert the initial problem into a new problem by using suitable transformations, in which the time-dependent unknown function is transferred to the boundary conditions, and then we provide a spectral approximation based on the Ritz method to detect the unknown functions. The discretization of the problem using the presented technique leads to a system of linear algebraic equations which is solved by employing the Tikhonov's regularization method. The numerical simulation results confirm the acceptable accuracy and stability of the approximate solution.
Keywords: Inverse problem of fourth-order parabolic equation, Tikhonov regularization, spectral method, orthonormal Bernstein basis functions.
Type of Study: Original Manuscript |
Subject:
Anal
Received: 2022/10/22 | Revised: 2024/04/7 | Accepted: 2023/09/10 | Published: 2024/01/8 | ePublished: 2024/01/8
Received: 2022/10/22 | Revised: 2024/04/7 | Accepted: 2023/09/10 | Published: 2024/01/8 | ePublished: 2024/01/8
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