Abstract
For evolution problems, the approximate solution on the upper time level is often obtained from a number of simpler problems. Standard splitting schemes use an additive splitting of the problem operator into operators more convenient for computational implementation and time implicit-explicit approximations. In the present paper, we consider a new class of splitting schemes associated with an additive representation of the solution itself rather than of the problem operator. We suggest a new general solution splitting procedure based on an additive representation of the identity operator via restriction and extension operators for auxiliary spaces. Unconditionally stable splitting schemes for the approximate solution of the Cauchy problem for a second-order evolution equation in a finite-dimensional Hilbert space are constructed and studied.
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This work was financially supported by the Government of the Russian Federation, agreement no. 14.Y26.31.0013.
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Translated by V. Potapchouck
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Vabishchevich, P.N. Solution Decomposition Schemes for Second-Order Evolution Equations. Diff Equat 57, 848–856 (2021). https://doi.org/10.1134/S0012266121070028
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DOI: https://doi.org/10.1134/S0012266121070028