caa a22 4500 60552436X CHVBK 20210128100753.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10958-015-2322-8 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2322-8 Reduction of A Three-Layer Semi-Discrete Scheme for an Abstract Parabolic Equation to Two-Layer Schemes. Explicit Estimates for the Approximate Solution Error [Elektronische Daten] [J. Rogava, D. Gulua] 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. Springer Science+Business Media New York, 2015 Rogava J. I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia aut Gulua D. Georgian Technical University, Tbilisi, Georgia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/4(2015-04-01), 424-444 1072-3374 206:4<424 2015 206 10958 https://doi.org/10.1007/s10958-015-2322-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2322-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rogava J. I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia aut NATIONALLICENCE 700 1- Gulua D. Georgian Technical University, Tbilisi, Georgia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/4(2015-04-01), 424-444 1072-3374 206:4<424 2015 206 10958