  On the basis of additive schemes (splitting schemes) we construct efficient
numerical algorithms to solve approximately the initial-boundary value problems
for systems of time-dependent partial differential equations (PDEs). In many
applied problems the individual components of the vector of unknowns are
coupled together and then splitting schemes are applied in order to get a
simple problem for evaluating components at a new time level. Typically, the
additive operator-difference schemes for systems of evolutionary equations are
constructed for operators coupled in space. In this paper we investigate more
general problems where coupling of derivatives in time for components of the
solution vector takes place. Splitting schemes are developed using an additive
representation for both the primary operator of the problem and the operator at
the time derivative. Splitting schemes are based on a triangular two-component
representation of the operators.
