The initial value problem for hyperbolic equations d 2u(t)/dt 2+A u(t)=f(t)(0≤t≤1),u(0)=φ,u′(0)=ψ, in
a Hilbert space H is considered. The first and second order
accuracy difference schemes generated by the integer power of A
approximately solving this initial value problem are presented.
The stability estimates for the solution of these difference
schemes are obtained.