  Studies of quasinormal modes (QNMs) of black holes have a long and well
established history. Predominantly, much research in this area has customarily
focused on the equations given by Regge, Wheeler and Zerilli. In this work we
study linearized perturbations of a Schwarzschild black hole using the
Characteristic formulation of numerical relativity, with an emphasis on the
computation of QNMs. Within this formalism, the master equation describing
gravitational perturbations is known to satisfy a fourth order hypergeometric
differential equation. We analyse the singular points of this master equation,
and obtain series solutions whose coefficients are given by three term
recurrence relations, from which Leaver's continued fraction method can be
applied. Using this technique, we recover the standard Schwarzschild
quasinormal modes. In addition, we find that imposing purely outgoing boundary
conditions, a natural feature of the Bondi-Sachs framework, leads to the
recovery of the algebraically special mode.
