  We propose a simple and computationally fast method for performing N-body
simulations for a large class of modified gravity theories with a screening
mechanism such as chameleons, symmetrons and galileons. By combining the linear
Klein-Gordon equation with a screening factor, calculated from analytical
solutions of spherical symmetric configurations, we obtain a modified field
equation whose solution is exact in the linear regime while at the same time
takes screening into account on non-linear scales. The resulting modified field
equation remains linear and can be solved just as quickly as the Poisson
equation without any of the convergence problems that can arise when solving
the full equation. We test our method with N-body simulations and find that it
compares remarkably well with full simulations well into the non-linear regime.
