  The gravitational shift of electromagnetic frequency in the strong field
limit is usually investigated under the common scenario, where the light
receiver is far away from the central body while the emitter is in the
strong-field region of the lens. In this paper, the gravitational frequency
shift of light caused by a Reissner-Nordstr\"{o}m (RN) black hole is studied
numerically in the traditional strong-field scenario, as well as in the
scenario where both the light emission and reception events happen in the
strong-field region of the black hole. In order to obtain the numerical results
of the gravitational redshift, we first derive the exact null equations of
motion in the RN geometry in harmonic coordinates. For a given light observer,
a new numerical technique is proposed in the integration of the geodesic
equations to determine the spatial position of the emitter, considering the
fact that their spatial positions are not always known simultaneously. Our work
might be helpful to the related observations for probing strong gravity.
