Contemporary Methods for the Numerical-Analytic Solution of Boundary-Value Problems in Noncanonical Domains

Autor: Vyacheslav V. Popov, V. T. Grinchenko, P. Shakeri Mobarakeh, G. M. Zrazhevsky, Babak Soltannia
Rok vydání: 2020
Předmět:
Zdroj: Journal of Mathematical Sciences. 247:88-107
ISSN: 1573-8795
1072-3374
DOI: 10.1007/s10958-020-04791-4
Popis: As an example of application of the contemporary numerical-analytic methods to the solution of boundary-value problems in noncanonical domains, we consider the Dirichlet boundary-value problem of the potential theory in the domain bounded by a parallelogram. The simplicity and clarity of the procedure used for the construction of the solution enable us to clearly illustrate some specific features of the contemporary approaches to the solution of various problems of mathematical physics. For numerous types of regions including a broad range of noncanonical domains, the application of the notion of general solution of the boundary-value problem enables one to construct its numerical-analytic solution. In this case, the researchers use the well-known collections of partial solutions of the basic equations of mathematical physics. The main problem is to indicate efficient ways that can be used to determine arbitrary coefficients and functions appearing in the general solution. Note that the application of the traditional approach according to which the numerical-analytic solutions are obtained on the basis of minimization of standard deviations often leads to cumbersome calculations in the case of noncanonical domains. As an alternative to this method, we can mention the contemporary method of boundary integral equations. The present work is devoted to the development of the indicated two approaches to the solution of the boundary-value problems and their comparison.
Databáze: OpenAIRE
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