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Identifying an unknown potential term in the fourth-order Boussinesq–Love equation from mass measurement

M.J. Huntul (Department of Mathematics, Jazan University, Jazan, Saudi Arabia)
Mohammad Tamsir (Department of Mathematics, Jazan University, Jazan, Saudi Arabia)

Engineering Computations

ISSN: 0264-4401

Article publication date: 24 May 2021

Issue publication date: 7 December 2021

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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

Copyright © 2021, Emerald Publishing Limited

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