Identifying an unknown potential term in the fourth-order Boussinesq–Love equation from mass measurement
ISSN: 0264-4401
Article publication date: 24 May 2021
Issue publication date: 7 December 2021
Abstract
Purpose
The inverse problem of identifying the time-dependent potential coefficient along with the temperature in the fourth-order Boussinesq–Love equation (BLE) with initial and boundary conditions supplemented by mass measurement is, for the first time, numerically investigated. From the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.
Design/methodology/approach
For the numerical discretization, the authors apply the Crank–Nicolson finite difference method along with the Tikhonov regularization for finding a stable and accurate approximate solution. The resulting nonlinear minimization problem is solved using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.
Findings
The present computational results demonstrate that obtained solutions are stable and accurate.
Originality/value
The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical identification has been studied yet. Therefore, the main aim of the present work is to undertake the numerical realization. The von Neumann stability analysis is also discussed.
Keywords
Citation
Huntul, M.J. and Tamsir, M. (2021), "Identifying an unknown potential term in the fourth-order Boussinesq–Love equation from mass measurement", Engineering Computations, Vol. 38 No. 10, pp. 3944-3968. https://doi.org/10.1108/EC-12-2020-0757
Publisher
:Emerald Publishing Limited
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