David Gulua

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

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