In this paper we consider the inital-boundary value problems for second order linear hyperbolic equations with variable coefficientswhere x = (x1,...,xp), two alternating-direction schemes are established for these problems. Stability and convergence of these schemes are also given. The method used is to establish energy inequalities for the solutions of difference schemes. The behaviour of these schemes is analogous to that of usual alternating-direction methods for heat flow problems.
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