  We examine the stability of the Garfinkle-Horowitz-Strominger (GHS) black
hole under charged scalar perturbations. We find that different from the
neutral scalar field perturbations, only two numerical methods, such as the
continued fraction method and the asymptotic iteration method, can keep high
efficiency and accuracy requirements in the frequency domain computations. The
comparisons of the efficiency between these two methods have also been done.
Employing the appropriate numerical method, we show that the GHS black hole is
always stable against charged scalar perturbations. This is different from the
result obtained in the de Sitter and Anti-de Sitter black holes. Furthermore we
argue that in the GHS black hole background there is no amplification of the
incident charged scalar wave to cause the superradiance, so that the
superradiant instability cannot exist in this spacetime.
