  An explicit stabilized additive Runge-Kutta scheme is proposed. The method is
based on a splitting of the problem in severely stiff and mildly stiff
subproblems, which are then independently solved using a Runge-Kutta-Chebyshev
scheme. The number of stages is adapted according to the subproblem's stiffness
and leads to asynchronous integration needing ghost values. Whenever ghost
values are needed, linear interpolation in time between stages is employed. One
important application of the scheme is for parabolic partial differential
equations discretized on a nonuniform grid. The goal of this paper is to
introduce the scheme and prove on a model problem that linear interpolations
trigger instabilities into the method. Furthermore, we show that it suffers
from an order reduction phenomenon. The theoretical results are confirmed
numerically.
