  Cauchy problem for an abstract hyperbolic equation with the Lipschitz
continuous operator is considered in the Hilbert space. The operator
corresponding to the elliptic part of the equation is a sum of operators
$A_{1},\,A_{2},\,\ldots,\,A_{m}$. Each addend is a self-adjoint and positive
definite operator. A parallel type decomposition scheme for an approximate
solution of the stated problem is constructed. The main idea of the scheme is
that on each local interval classic difference problems are solved in parallel
(independently from each other) respectively with the operators
$A_{1},\,A_{2},\,\ldots,\,A_{m}$. The weighted average of the received
solutions is announced as an approximate solution at the right end of the local
interval. Convergence of the proposed scheme is proved and the approximate
solution error is estimated, as well as the error of the difference analogue
for the first-order derivative for the case when the initial problem data
satisfy the natural sufficient conditions for solution existence.
