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We present an equation-free multi-scale approach to the computational studyof the collective dynamics of the Kuramoto model [{\it Chemical Oscillations,Waves, and Turbulence}, Springer-Verlag (1984)], a prototype model for coupledoscillator populations. Our study takes place in a reduced phase space ofcoarse-grained "observables" of the system: the first few moments of theoscillator phase angle distribution. We circumvent the derivation of explicitdynamical equations (approximately) governing the evolution of thesecoarse-grained macroscopic variables; instead we use the {\it equation-freeframework} [Kevrekidis {\it et al.}, {\it Comm. Math. Sci.} {\bf 1}(4), 715(2003)] to computationally solve these equations without obtaining them inclosed form. In this approach, the numerical tasks for the conceptuallyexisting but unavailable coarse-grained equations are implemented through shortbursts of appropriately initialized simulations of the "fine-scale", detailedcoupled oscillator model. Coarse projective integration and coarse fixed pointcomputations are illustrated.Comment: submitted to the {\it International Journal of Bifurcations and  Chaos

AN EQUATION-FREE APPROACH TO COUPLED OSCILLATOR DYNAMICS: THE KURAMOTO MODEL EXAMPLE