Inverse Problem for Coefficient Identification in Euler-Bernoulli Equation by Linear Spline Approximation

We display the performance of the technique called Method of Variational Imbedding for solving the inverse problem of coefficient identification in Euler-Bernoulli equation from over-posed data. The original inverse problem is replaced by a minimization problem. The EulerLagrange equations comprise an eight-order equation for the solution of the original equation and an explicit system of equations for the coefficients of the spline approximation of the unknown coefficient. Featuring examples are elaborated numerically. The numerical results confirm that the solution of the imbedded problem coincides with the exact solution of the original problem within the order of approximation error.