  Many applied time-dependent problems are characterized by an additive
representation of the problem operator. Additive schemes are constructed using
such a splitting and associated with the transition to a new time level on the
basis of the solution of more simple problems for the individual operators in
the additive decomposition. We consider a new class of additive schemes for
problems with additive representation of the operator at the time derivative.
In this paper we construct and study the vector operator-difference schemes,
which are characterized by a transition from one initial the evolution equation
to a system of such equations.
