The abstract initial value perturbation problem $\epsilon^2u''(t) + Au(t) = f(t), 0 < t < T,$  $u(0) = \phi, u'(0) = \Psi$ for hyperbolic equations is studied. The self adjoint positive definite operator $A$ in a Hilbert space $H$ is considered. An arbitrarily small parameter $\epsilon\in (0, \infty)$ multiplying the highest derivative term is considered. An asymptotic solution to the problem is presented. The uniform high-order two-step difference schemes corresponding to this problem are obtained. This work covers the general perturbation theory of uniform difference schemes on hyperbolic partial differential equations. The theoretical results are verified by the numerical implementations using Matlab. The error results of the numerical experiments are also presented. This is a joint work with Prof. Dr. Allaberen Ashyralyev (BAU).