Identification hyperbolic problems with the Neumann boundary condition

In the present study, an identification problem with the Neumann boundary condition for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the identification problem are established. Furthermore, a first order of accuracy difference scheme for the numerical solution of the identification problems for hyperbolic equations with the Neumann boundary condition is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example and some numerical results are presented.