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- W2953943313 abstract "The block element method (Babeshko in Ecol Bull Res Centers Black Sea Econ Coop (BSEC) 2:13, 2014, [1]), which was elaborated by V. A. Babeshko and developed by his disciples, makes it possible to solve boundary-value problems stated for arbitrary convex domains and described in terms of arbitrary linear systems of differential equations in finite-order partial derivatives. The boundary-value problems are assumed to be properly stated. The domains can be bounded, semi-bounded and unbounded. Moreover, the method can be applied to the finite aggregate of domains, which interact over shared boundaries. According to the block element method, the boundary-value problem is set in the topological space and reduced to the system of functional equations using external analysis tools. From the pseudo-differential equations obtained due to differential factorization and automorphism, integral equations are extracted, which correspond to certain boundary conditions. A large number of variations of the block element method have been developed so far for the three-dimensional setting of boundary-value problems for various mathematical physics equations. The method is highly versatile, however, it requires the knowledge of topology, differential geometry, multidimensional complex analysis, external analysis, i.e. the disciplines, which are normally not included in the standard mathematics curricular at the university level. To increase the comprehension of the method, it is necessary for scientific and methodological purposes to study in detail how comparatively simple problems are solved by this method. The research provides a detailed algorithm of the block element for the model boundary-value problem, which is described by the Bessel equation for the circular domain." @default.
- W2953943313 created "2019-07-12" @default.
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- W2953943313 date "2019-01-01" @default.
- W2953943313 modified "2023-10-17" @default.
- W2953943313 title "Block Element with a Circular Boundary" @default.
- W2953943313 cites W629880307 @default.
- W2953943313 doi "https://doi.org/10.1007/978-3-030-19894-7_32" @default.
- W2953943313 hasPublicationYear "2019" @default.
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