2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222771The main aim of this study is the comparison of gravitational waveforms obtained from numerical simulations which employ different numerical evolution approaches and different wave-extraction techniques. For this purpose, we evolve an oscillating, non-rotating polytropic neutron-star model with two different approaches: a full nonlinear relativistic simulation (in three dimensions) and a linear simulation based on perturbation theory. The extraction of the gravitational-wave signal is performed with three methods: The gauge-invariant curvature-perturbation theory based on the Newman-Penrose scalar $ψ_4$; The gauge-invariant Regge-Wheeler-Zerilli-Moncrief metric-perturbation theory of a Schwarzschild space-time; Some generalization of the quadrupole emission formula.27 pages, 18 figures. Published in Phys. Rev. DGeneral Relativity and Quantum CosmologyAstrophysicstext