Splitting Schemes for Evolution Equations with a Factorized Operator

In the approximate solution of the Cauchy problem for evolution equations, the problemoperator can often be represented as a sum of simpler operators. This makes it possible toconstruct operator-difference splitting schemes, when the transition to a new level in time isprovided by solving problems for separate operator terms. We consider nonstationary problemswhose main feature is related to the representation of the problem operator as a product of theoperator \(A\) by the adjoint operator \(A^*\) . Based on the transformation of the originalequation to a system of two equations, we construct time approximations for second-orderevolution equations when the additive representation holds for the operator \(A\) . Unconditional stable splitting schemes areproposed whose study is carried out with the help of general results of the theory of stability(well-posedness) of operator-difference schemes in Hilbert spaces.