Abstract

The nonlocal boundary value problem for hyperbolic-elliptic equation d2u(t)/dt2+Au(t)=f(t), (0t1), d2u(t)/dt2+Au(t)=g(t), (1t0), u(0)=ϕ, u(1)=u(1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established.