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Identifying the Inverse Force Problem for the Beam Equation With Boundary Conditions at a Single Point in Space or Time.

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Title: Identifying the Inverse Force Problem for the Beam Equation With Boundary Conditions at a Single Point in Space or Time.
Authors: Mahmood, Shirin I.1,2 (AUTHOR), Hussein, Shilan O.1 (AUTHOR) shilan.husen@univsul.edu.iq, Dyhoum, Taysir E.3,4 (AUTHOR), Habib, Mohammad Rezwan (AUTHOR) mohabib@wiley.com
Source: Journal of Applied Mathematics. 5/12/2026, Vol. 2026, p1-12. 12p.
Subjects: Inverse problems, Finite difference method, Euler-Bernoulli beam theory, Boundary value problems, Numerical analysis, Stability theory, Tikhonov regularization, Iterative methods (Mathematics)
Abstract: We analyze an inverse force problem that involves identifying a source term in a one‐dimensional fourth‐order beam equation depending on either space or time. Mixed boundary conditions and an overdetermination condition based on a single point in space or time address the problem. For both direct and inverse problems, we rely on the existence and uniqueness theorems from previous research. Likewise, we apply the Von Neumann method to determine stability. The finite difference method (FDM) with Tikhonov regularization effectively identifies displacement and source problems in numerical analysis. Consequently, a small amount of noise improves the accuracy and consistency of the final results, as demonstrated by tests conducted at various noise levels. Numerical experiments with both exact and noisy data show the accuracy, reliability, and efficiency of our approach. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Identifying the Inverse Force Problem for the Beam Equation With Boundary Conditions at a Single Point in Space or Time.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 5/12/2026, Vol. 2026, p1-12. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Euler-Bernoulli+beam+theory%22">Euler-Bernoulli beam theory</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Tikhonov+regularization%22">Tikhonov regularization</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
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  Data: We analyze an inverse force problem that involves identifying a source term in a one‐dimensional fourth‐order beam equation depending on either space or time. Mixed boundary conditions and an overdetermination condition based on a single point in space or time address the problem. For both direct and inverse problems, we rely on the existence and uniqueness theorems from previous research. Likewise, we apply the Von Neumann method to determine stability. The finite difference method (FDM) with Tikhonov regularization effectively identifies displacement and source problems in numerical analysis. Consequently, a small amount of noise improves the accuracy and consistency of the final results, as demonstrated by tests conducted at various noise levels. Numerical experiments with both exact and noisy data show the accuracy, reliability, and efficiency of our approach. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
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        Value: 10.1155/jama/1929753
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      – Code: eng
        Text: English
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        PageCount: 12
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      – SubjectFull: Inverse problems
        Type: general
      – SubjectFull: Finite difference method
        Type: general
      – SubjectFull: Euler-Bernoulli beam theory
        Type: general
      – SubjectFull: Boundary value problems
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      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: Tikhonov regularization
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
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      – TitleFull: Identifying the Inverse Force Problem for the Beam Equation With Boundary Conditions at a Single Point in Space or Time.
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          Name:
            NameFull: Mahmood, Shirin I.
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            NameFull: Hussein, Shilan O.
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            NameFull: Dyhoum, Taysir E.
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              M: 05
              Text: 5/12/2026
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              Y: 2026
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