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 non-zero but cancel each other,
 (217)
the adding of the operator gives equilibrium Eq. (216), while operator splitting
 (218)
This is not necessarily a stationary solution. Here, operator adding is superior.