The aim of this work is to identify numerically, for the first time, the time-dependent potential coefficient in a fourth-order pseudo-parabolic equation with nonlocal initial data, nonlocal boundary conditions, and the boundary data as overdetermination condition. This problem emerges significantly in the modeling of various phenomena in physics and engineering. From literature we 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. For the numerical realization, we apply the quintic B-spline (QB-spline) collocation method for discretizing the pseudo-parabolic problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved using the MATLAB subroutine lsqnonlin. Moreover, the von Neumann stability analysis is also discussed.

中文翻译：

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从附加条件识别四阶伪抛物方程中的时间相关势的反问题

这项工作的目的是首次以数值方式识别具有非局部初始数据、非局部边界条件和边界数据作为超定条件的四阶伪抛物线方程中的时间相关势系数。这个问题在物理和工程中的各种现象的建模中显着出现。从文献中我们已经知道这个逆问题有一个唯一的解决方案。但是，由于对输入数据中的噪声不稳定，该问题仍然不适定。对于数值实现，我们应用五次 B 样条 (QB-spline) 搭配方法来离散化伪抛物线问题，并应用 Tikhonov 正则化来寻找稳定和准确的解。使用 MATLAB 子例程解决了由此产生的非线性最小化问题lsqnonlin。此外，还讨论了冯诺依曼稳定性分析。