This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to discretize the hyperbolic fourth-order equation. A stability analysis for the proposed scheme is also provided. The indirect problem is the minimization of the misfit function. The goal of the minimization algorithm is to reduce the gap between the measured (noisy) data and the numerical computed solution provided by the model. To achieve stable results, Tikhonov’s regularization technique is employed, and two numerical test examples are shown to illustrate the suggested scheme's reliabilit

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

In this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.