Recovery of timewise‐dependent heat source for hyperbolic PDE from an integral condition

Huntul, M. J.; Tamsir, Mohammad

doi:10.1002/mma.6845

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…The inverse problem for identifying time- and/or space-wise coefficients in the second-order hyperbolic equations have been studied in Bui (2003), Cannon and DuChateau (1983), Eskin (2017), Jiang et al. (2017), Hasanov and Romanov (2017), Huntul and Tamsir (2021a), Ramm and Rakesh (1991), Salazar (2013), Stefanov and Uhlmann (2013), Tekin (2019a) and Yamamoto (1995). However, adequate investigations of the inverse problems for the second-order hyperbolic equation have been studied, yet the studied on inverse problems for the pseudo-hyperbolic equations are insufficient.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

Huntul

Tamsir

2022

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PurposeThe purpose of this paper is to reconstruct the potential numerically in the fourth-order Rayleigh–Love equation with boundary and nonclassical boundary conditions, from additional measurement.Design/methodology/approachAlthough, the aforesaid inverse identification problem is ill-posed but has a unique solution. The authors use the cubic B-spline (CBS) collocation and Tikhonov regularization techniques to discretize the direct problem and to obtain stable as well as accurate solutions, respectively. The stability, for the discretized system of the direct problem, is also carried out by means of the von Neumann method.FindingsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Research limitations/implicationsSince the noisy data are introduced, the investigation and analysis model real circumstances where the practical quantities are naturally infested with noise.Practical implicationsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Originality/valueThe potential term in the fourth-order Rayleigh–Love equation from additional measurement is reconstructed numerically, for the first time. The technique establishes that accurate, as well as stable solutions are obtained.

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Section: Introductionmentioning

confidence: 99%

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

Huntul

Tamsir

2022

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“…In [10,11,20], authors recovered the time-and space-dependent source functions. Huntul and Tamsir [16] investigated an inverse problem to recover a time-wise heat source from the integral condition. Still, the inverse problem of reconstructing the time-wise potential coefficient numerically for the hyperbolic problems with integral and periodic BCs is inadequate in the literature.…”

Section: Introductionmentioning

confidence: 99%

An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

2021

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In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

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Solutions for non-homogeneous wave equations subject to unusual and Neumann boundary conditions

Hussein

Dyhoum

2022

Applied Mathematics and Computation

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Recovery of timewise‐dependent heat source for hyperbolic PDE from an integral condition

Cited by 7 publications

References 18 publications

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

Solutions for non-homogeneous wave equations subject to unusual and Neumann boundary conditions

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