Identification of time-dependent potential in a fourth-order pseudo-hyperbolic equation from additional measurement

The objective of this work is to reconstruct, for the first time, numerically the time-dependent potential coefficient in a fourth-order pseudo-hyperbolic equation with initial and boundary conditions from additional measurement as an overdetermination condition. This inverse identification problem is an ill-posed problem but has a unique solution. For the numerical realization, we apply the Quintic B-spline (QB-spline) collocation method to discretize the direct problem and the Tikhonov regularization to find a stable and accurate solution. The resulting nonlinear minimization problem is approximated using the MATLAB optimization toolbox routine lsqnonlin. The obtained numerical results are the evidence of the stable and accurate solutions. The von Neumann stability analysis is also carried out.