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.

中文翻译：

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从质量测量中识别四阶 Boussinesq-Love 方程中的未知电位项

目的

首次对以质量测量为补充的初始和边界条件的四阶 Boussinesq-Love 方程 (BLE) 中随时间变化的势能系数与温度的逆问题进行了数值研究。从文献中，作者已经知道这个逆问题有一个唯一的解决方案。然而，由于对输入数据中的噪声不稳定，问题仍然存在。

设计/方法/方法

对于数值离散化，作者应用 Crank-Nicolson 有限差分方法和 Tikhonov 正则化来寻找稳定且准确的近似解。使用 MATLAB 例程lsqnonlin解决由此产生的非线性最小化问题。精确的和数值模拟的噪声输入数据都被反转。

发现

目前的计算结果表明所获得的解是稳定和准确的。

原创性/价值

本文提出的逆问题已被证明是局部唯一可解的，但尚未研究数值识别。因此，目前工作的主要目的是进行数值实现。还讨论了冯诺依曼稳定性分析。