The inverse problem of identifying the time-dependent potential term along with the temperature in a third-order pseudo-parabolic equation with initial and Neumann boundary conditions supplemented by the additional condition is, for the first time, numerically investigated. This problem emerges significantly in the modelling of various phenomena in physics and engineering. Although, the inverse problem is ill-posed by being sensitive to noise but has a unique solution. For the numerical realization, we apply the cubic B-spline (CB-spline) collocation method for discretizing the direct problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB subroutine. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. The von Neumann stability analysis is also discussed.

首次在数值上研究了在带有初始条件和诺伊曼边界条件并附加了附加条件的三阶伪抛物方程中识别随时间变化的势项以及温度的反问题。这个问题在物理和工程学中的各种现象的建模中显着出现。虽然，反问题是由于对噪声敏感而引起的，但是具有独特的解决方案。对于数值实现，我们使用三次B样条（CB-spline）配置方法来离散直接问题，并使用Tikhonov正则化来找到稳定且准确的解决方案。由此产生的非线性最小化问题可以使用MATLAB子例程进行计算解决。给出的两个示例的数值结果表明，即使在输入数据中存在噪声的情况下，计算方法的效率以及数值解的准确性和稳定性。还讨论了冯·诺依曼稳定性分析。