  The present study concerns the numerical homogenization of second order
hyperbolic equations in non-divergence form, where the model problem includes a
rapidly oscillating coefficient function. These small scales influence the
large scale behavior, hence their effects should be accurately modelled in a
numerical simulation. A direct numerical simulation is prohibitively expensive
since a minimum of two points per wavelength are needed to resolve the small
scales. A multiscale method, under the equation free methodology, is proposed
to approximate the coarse scale behaviour of the exact solution at a cost
independent of the small scales in the problem. We prove convergence rates for
the upscaled quantities in one as well as in multi-dimensional periodic
settings. Moreover, numerical results in one and two dimensions are provided to
support the theory.
