Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

In the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.