Abstract:
A unified method for constructing basis (eigen) functions is proposed to solve problems of mechanics of continuous media, problems of cubature and quadrature, and problems of approximation of hypersurfaces. Numerical-analytical methods are described, which allow obtaining approximate solutions of internal and external boundary-value problems of mechanics of continuous media of a certain class (both linear and nonlinear). The method is based on decomposition of the sought solutions of the considered partial differential equations into series in basis functions. An algorithm is presented for linearization of partial differential equations and reduction of nonlinear boundary-value problems, which are reduced to systems of linear algebraic equations with respect to unknown coefficients without using traditional methods of linearization.
Citation:
G. V. Druzhinin, “Construction of basis functions and their application to boundary-value problems of mechanics of continuous media”, Prikl. Mekh. Tekh. Fiz., 44:6 (2003), 35–43; J. Appl. Mech. Tech. Phys., 44:6 (2003), 779–785
\Bibitem{Dru03}
\by G.~V.~Druzhinin
\paper Construction of basis functions and their application to boundary-value problems of mechanics of continuous media
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2003
\vol 44
\issue 6
\pages 35--43
\mathnet{http://mi.mathnet.ru/pmtf2555}
\elib{https://elibrary.ru/item.asp?id=17274847}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2003
\vol 44
\issue 6
\pages 779--785
\crossref{https://doi.org/10.1023/A:1026223418219}
Linking options:
https://www.mathnet.ru/eng/pmtf2555
https://www.mathnet.ru/eng/pmtf/v44/i6/p35
This publication is cited in the following 2 articles:
N M Bodunov, V I Khaliulin, “Poisson bracket and integrals of motion in the problem of viscous fluid flow around an arbitrary flat contour”, J. Phys.: Conf. Ser., 1679:3 (2020), 032086
N. M. Bodunov, G. V. Druzhinin, “One solution of an axisymmetric problem of the elasticity theory for a transversely isotropic material”, J. Appl. Mech. Tech. Phys., 50:6 (2009), 982–988
Citation in format AMSBIB
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