An inverse problem of identifying the time-dependent potential in a fourth-order pseudo-parabolic equation from additional condition

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.