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Vector domain decomposition schemes for parabolic equations

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Abstract

A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, Moscow, 115191, Russia

    P. N. Vabishchevich

  2. Ammosov North-Eastern Federal University, Yakutsk, 677000, Russia

    P. N. Vabishchevich

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  1. P. N. Vabishchevich
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Original Russian Text © P.N. Vabishchevich, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 9, pp. 1530–1547.

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Vabishchevich, P.N. Vector domain decomposition schemes for parabolic equations. Comput. Math. and Math. Phys. 57, 1511–1527 (2017). https://doi.org/10.1134/S0965542517090135

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  • DOI: https://doi.org/10.1134/S0965542517090135

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