  This paper considers computational methods that split a vector field into
three components in the case when both the vector field and the split
components might be unbounded. We first employ classical Taylor expansion
which, after some algebra, results in an expression for a second-order
splitting which, strictly speaking, makes sense only for bounded operators.
Next, using an alternative approach, we derive an error expression and an error
bound in the same setting which are however valid in the presence of unbounded
operators.
  While the paper itself is concerned with second-order splittings using three
components, the method of proof in the presence of unboundedness remains valid
(although significantly more complicated) in a more general scenario, which
will be the subject of a forthcoming paper.
