Volume 9, Issue 4 (12-2023)
mmr 2023, 9(4): 225-239 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Rashedi K. Numerical solution of an inverse problem for fourth order parabolic equation with integral boundary condition using operational matrices. mmr 2023; 9 (4) :225-239
URL: http://mmr.khu.ac.ir/article-1-3295-en.html
URL: http://mmr.khu.ac.ir/article-1-3295-en.html
University of Science and Technology of Mazandaran , k.rashedi@mazust.ac.ir
Abstract: (1046 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: 2024/06/23 | Accepted: 2023/09/10 | Published: 2024/01/8 | ePublished: 2024/01/8
Received: 2022/10/22 | Revised: 2024/06/23 | Accepted: 2023/09/10 | Published: 2024/01/8 | ePublished: 2024/01/8
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
