Reduction of a three-layer semi-discrete scheme for an abstract parabolic equation to two-layer schemes. Explicit estimates for the approximate solution error

We consider a purely implicit three-layer semi-discrete approximation scheme of second order for an approximate solution of the Cauchy problem for an abstract parabolic equation. Using the perturbation algorithm, we reduced this scheme to two two-layer schemes. The solutions of these schemes are used for the construction of an approximate solution of the initial problem. Explicit estimates for the approximate solution error are proved using the properties of a semi-group. To illustrate the generality of the perturbation algorithm when it is applied to difference schemes, a fourlayer scheme reduced to two-layer schemes is also considered.