Inverse problem for coefficient identification in the Euler–Bernoulli equation

A special technique has been developed for the identification of the solution and the unknown coefficient in the Euler–Bernoulli equation. The original problem of the unknown coefficient identification from over-posed data is transferred into a higher-order well-posed problem following the idea of the Method of Variational Imbedding. The new boundary value problem is solved by means of an iterative finite difference scheme. The scheme is thoroughly validated and is shown to have a second-order truncation error.