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With the example of the spherically symmetric scalar wave equation onMinkowski space-time we demonstrate that a fully pseudospectral scheme (i.e.spectral with respect to both spatial and time directions) can be applied forsolving hyperbolic equations. The calculations are carried out within theframework of conformally compactified space-times. In our formulation, theequation becomes singular at null infinity and yields regular boundaryconditions there. In this manner it becomes possible to avoid "artificial"conditions at some numerical outer boundary at a finite distance. We obtainhighly accurate numerical solutions possessing exponential spectralconvergence, a feature known from solving elliptic PDEs with spectral methods.Our investigations are meant as a first step towards the goal of treating timeevolution problems in General Relativity with spectral methods in space andtime.

A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations