**Melnik (R.)V.N. **

__ __** Journal of Soviet Mathematics, 66(6), 2642-2652, 1993**

For the numerical solution of a coupled one-dimensional problem of dynamic thermoelasticity in stresses (deformations) we construct a difference scheme of second-order approximation. We study its stability and obtain an a priori estimate. We prove the convergence of the solution of the scheme to the generalized solution of the original problem in the Sobolev class $W^2_2(Q_T)$.