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The present study concerns the numerical homogenization of second orderhyperbolic equations in non-divergence form, where the model problem includes arapidly oscillating coefficient function. These small scales influence thelarge scale behavior, hence their effects should be accurately modelled in anumerical simulation. A direct numerical simulation is prohibitively expensivesince a minimum of two points per wavelength are needed to resolve the smallscales. A multiscale method, under the equation free methodology, is proposedto approximate the coarse scale behaviour of the exact solution at a costindependent of the small scales in the problem. We prove convergence rates forthe upscaled quantities in one as well as in multi-dimensional periodicsettings. Moreover, numerical results in one and two dimensions are provided tosupport the theory.

An Equation-Free Approach for Second Order Multiscale Hyperbolic Problems in Non-Divergence Form