About splitting semi-discrete scheme for an evolutionary equation with variable operator into two-layer schemes

Author: jemal rogava
Co-authors: R. Galdava, D. Gulua
Keywords: evolutionary equation, semi-discrete scheme, perturbation algorithm
Annotation:

In a Hilbert space we consider the Cauchy problem for an abstract parabolic equation with variable, self-adjoint, positively defined operator. For approximate solution of this problem, using the perturbation algorithm, implicit three-layer semi-discrete scheme is reduced to two-layer schemes. An approximate solution of the original problem is constructed by means of the solutions of these schemes. The approximate solution error is estimated.