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In this paper we present in detail the numerical solution of the conformallyinvariant wave equation on top of a fixed background space-time correspondingto two different cases: i) 1+1 Minkowski space-time in Cartesian coordinatesand ii) Schwarzschild space-time. In both cases we use hyperboloidal constantmean curvature slices and scri-fixing conformal compactification, and solve thewave equation on the conformal space-time. In the case of the Schwarzschildspace-time we study the quasinormal mode oscillations and the late-timepolynomial tail decay exponents corresponding to a mass-less scalar field. Wealso present general formulas to construct hyperboloidal constant meancurvature slicings of spherically symmetric, static, space-times in sphericalcoordinates.

Numerical solution of the wave equation on particular space-times using CMC slices and scri-fixing conformal compactification