  Self-consistent relativistic random-phase approximation (RPA) in the radial
coordinate representation is established by using the finite amplitude method
(FAM). Taking the isoscalar giant monopole resonance in spherical nuclei as
example, the feasibility of the FAM for the covariant density functionals is
demonstrated, and the newly developed methods are verified by the conventional
RPA calculations. In the present relativistic RPA calculations, the effects of
the Dirac sea can be automatically taken into account in the coordinate-space
representation. The rearrangement terms due to the density-dependent couplings
can be implicitly calculated without extra computational costs in both
iterative and matrix FAM schemes.
