I will briefly present an efficient class of numerical methods to solve partial differential equations : the spectral method. I will in particular focus on a rather general tool that implements those methods : the Kadath library. I will then present two applications. First I will show results on boson stars, a class of self-gravitating objects that are a possible alternative to the black hole model. Second, I will discuss the nature of self-trapped packet of gravitational waves, in the presence of a negative cosmological constant: the so-called gravitational geons.