SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FACTORIZED OPERATOR

In the approximate solution of the Cauchy problem for evolution equations, the problem operator can often be represented as a sum of simpler operators. This makes it possible to construct operatordifference splitting schemes, when the transition to a new level in time is provided by solving problems for separate operator summands. We consider nonstationary problems, the main feature of which is related to the representation of the problem operator as a product of the operator 𝐴 by its conjugate operator 𝐴*. Based on the transformation of the original equation to a system of two equations, we construct time approximations for second-order evolutionary equations when the additive representation holds for the operator 𝐴. Unconditional stable splitting schemes are proposed, the study of which is carried out with the help of general results of the theory of stability (correctness) of operator-difference schemes in Hilbert spaces.