  In many cases, analytic solutions of partial differential equations may not
be possible. For practical problems, it is more reasonable to carry out
computational solutions. However, the standard grid in the finite difference
approximation is not a correct model of the continuous domain in terms of
digital topology. In order to avoid serious problems in computational solutions
it is necessary to use topologically correct digital domains. This paper
studies the structure of the hyperbolic partial differential equation on graphs
and digital n-dimensional manifolds, which are digital models of continuous
n-manifolds. Conditions for the existence of solutions are determined and
investigated. Numerical solutions of the equation on graphs and digital
n-manifolds are presented.
