Splitting Schemes for Evolution Equations with a Factorized Operator

Abstract

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 by the adjoint operator. 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. 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.