On a new class of additive (splitting) operator-difference schemes

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.