  In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method
for the numerical solution of ODEs is presented.
  This methods can be regarded as an approximate formulation of the Taylor
methods and it follows an approach that has a much easier implementation than
the original Taylor methods, since only the functions in the ODEs, and not
their high order derivatives, are needed. In this reference, the absolute
stability region of the new methods is conjectured to be coincident with that
of their exact counterparts. There is also a conjecture about their
relationship with Runge-Kutta methods. In this work we answer positively both
conjectures.
