The shooting method employed to compute the steady-state solution of circuits in the time domain is well known, largely used, and has been intensely studied in the literature. During these last decades, the large penetration of radio-frequency devices in the everyday activities has renewed some interest in this method, but the renewed interest is mainly focused on the simulation of large or very large circuits composed of thousands of transistors. The original formulation of the shooting method, despite being formally adequate, is unfeasible to handle this target. The introduction of iterative methods such as for example GMRES has largely pushed up the maximum size of the circuits that can be considered. Nevertheless, this may be not enough. We present an approach that faces the curse of dimensionality suffered by the original method. It allows both saving memory occupation and tackling circuits (or systems) with a number of differential and algebraic variables well above those managed by GMRES. Dimensionality is reduced by exploiting Galerkin projections.