On the absolute stable difference scheme for the space-wise dependent source identification problem for elliptic-telegraph equation

The present paper is devoted to study the first order of accuracy absolute stable difference scheme for the approximate solution of the space identification problem for the elliptic-telegraph equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the difference scheme is established. In applications, theorems on the stability of difference schemes for two types of the space identification problems for multidimensional elliptic-telegraph partial differential equations are proved. Numerical analysis is provided.