Reduction of a Four-Layer Semi-Discrete Scheme for an Abstract Evolution Equation to Two-Layer Schemes and Estimation of the Approximate Solution Errors by Using Associated Polynomials

摘要

In the paper, a purely implicit four-layer semi-discrete scheme for an abstract evolution equation is reduced by means of an perturbation algorithm to two-layers schemes. Based on the latter schemes, an approximate solution of the initial problem is constructed. The approximate solution error estimate is obtained in the Hilbert space by using associated polynomials.