  In this work we study operator splitting methods for a certain class of
coupled abstract Cauchy problems, where the coupling is such that one of the
problems prescribes a "boundary type" extra condition for the other one. The
theory of one-sided coupled operator matrices provides an excellent framework
to study the well-posedness of such problems. We show that with this machinery
even operator splitting methods can be treated conveniently and rather
efficiently. We consider three specific examples: the Lie (sequential), the
Strang and the weighted splitting, and prove the convergence of these methods
along with error bounds under fairly general assumptions.
