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Rogava, Jemal; Gulua, David

The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem. (English) Zbl 1453.65119

Georgian Math. J. 25, No. 1, 77-92 (2018).
Summary: In the present paper, we use the perturbation algorithm to reduce a purely implicit four-layer semi-discrete scheme for an abstract evolutionary equation to two-layer schemes. An approximate solution of the original problem is constructed using the solutions of these schemes. Estimates of the approximate solution error are proved in a Hilbert space.

Cited in 1 Document

MSC:

65J08 Numerical solutions to abstract evolution equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs

Keywords:

evolutionary problem; semi-discrete scheme; perturbation algorithm
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References:

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