Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity

We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial infinity, which is represented as a cylinder. We consider both Cauchy problems, where we evolve data from a Cauchy surface to future null infinity, as well as characteristic initial value problems with data at past null infinity, and demonstrate that highly accurate numerical solutions can be obtained for a small number of grid points.