Suppose both operators
and
are zero,

(214) 
resulting in individually
stationary solutions
(eg. hydrostatic and radiative equilibrium),

(215) 
which gives for both operator combination methods

(216) 
However, if the individual operators are nonzero but cancel each other,

(217) 
the adding of the operator gives equilibrium Eq. (216),
while operator splitting
This is not necessarily a stationary solution.
Here, operator adding is superior.