Reconstructing an unknown potential term in the third-order pseudo-parabolic problem

The inverse problem of identifying the time-dependent potential term along with the temperature in a third-order pseudo-parabolic equation with initial and Neumann boundary conditions supplemented by the additional condition is, for the first time, numerically investigated. This problem emerges sign...

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Veröffentlicht in:Computational & applied mathematics Jg. 40; H. 4
Hauptverfasser: Huntul, M. J., Dhiman, Neeraj, Tamsir, Mohammad
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Applied physics
Boundary conditions
Collocation methods
Computational mathematics
Computational Mathematics and Numerical Analysis
Inverse problems
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Noise sensitivity
Regularization
Stability analysis
Time dependence
Pseudo-parabolic equation
35K70
Nonlinear optimization
Inverse identification problem
65M30
Stability analysis
65M22
Tikhonov regularization
CB-spline collocation method
65M32
ISSN:2238-3603, 1807-0302
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Zusammenfassung:The inverse problem of identifying the time-dependent potential term along with the temperature in a third-order pseudo-parabolic equation with initial and Neumann boundary conditions supplemented by the additional condition is, for the first time, numerically investigated. This problem emerges significantly in the modelling of various phenomena in physics and engineering. Although, the inverse problem is ill-posed by being sensitive to noise but has a unique solution. For the numerical realization, we apply the cubic B-spline (CB-spline) collocation method for discretizing the direct problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB subroutine. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. The von Neumann stability analysis is also discussed.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01532-4