**David Gulua**

##
The Perturbation Algorithm for the Realization of a Multi-Layer Semi-Discrete
Solution Scheme for an Abstract Evolutionary Problem

**abstract:**

The paper presents the study of the Cauchy problem for an evolutionary equation
with a self-adjoint positive definite operator. Using the perturbation
algorithm, the purely implicit multi-layer semi-discrete solution scheme is
reduced to two-layer schemes. Solutions of the latter schemes are used for
constructing an approximate solution of the original problem. The estimate of
the approximate solution error is given.

**Mathematics Subject Classification:**
65J08, 65M12, 65M15, 65M55

**Key words and phrases:** Evolutionary problem, semi-discrete scheme,
multi-layer scheme, perturbation algorithm