Abstract—
A new rigorously substantiated approach is developed, which makes possible to expand significantly the class of boundary-value problems for the linear set of partial differential equations with constant coefficients in nonclassical domains, which can be solved exactly by the block-element method. Developed in the block-element method, a new coordinate complementing integro-differential method for satisfying boundary conditions completes the construction of exact solutions of the original boundary-value problems decomposed into block elements. This approach covers many sets of partial differential equations with constant coefficients in solid mechanics, hydromechanics, electromagnetic fields, and other sciences for which it is possible to construct exact solutions of boundary-value problems in nonclassical domains. Examples of implementing the approach are given.
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Funding
Selected parts of this study were carried out as part of the implementation of a State Assignment of the Ministry of Education and Science for 2021 (project no. FZEN-2020-0020), and the Federal Southern Science Center, Russian Academy of Sciences (project no. 00-20-13, state registration number 01201354241), and with the support of the Russian Foundation for Basic Research (project nos. 19-41-230003, 19- 41-230004, 19-48-230014, and 18-05-80008).
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Translated by V. Bukhanov
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Babeshko, V.A., Evdokimova, O.V. & Babeshko, O.M. Block Elements in Boundary-Value Problems for Sets of Differential Equations of Mechanics and Physics in Non-Classical Domains. Dokl. Phys. 66, 169–174 (2021). https://doi.org/10.1134/S102833582106001X
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DOI: https://doi.org/10.1134/S102833582106001X