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On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points
D. A. Shirobokov Dorodnicyn Computing Center, Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119991, Russia
Abstract:
The method of undetermined coefficients generates a set of fixed-order approximations of spatial derivatives on an irregular stencil. An additional condition is proposed that singles out a unique scheme from this set. The resulting second-to-fourth order accurate approximations are applied to solving Poisson's and the biharmonic equations. The bending of a plate supported by an edge, the nonlinear bending of a circular plate, and two-dimensional problems in solid mechanics are discussed. A method is proposed for constructing oriented approximations, which are validated by solving an advection equation.
Key words:
Poisson's equation, biharmonic equation, meshless methods, approximation of spatial derivatives.
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Computational Mathematics and Mathematical Physics, 2006, 46:6, 1023–1043
Bibliographic databases:
UDC:
519.634 Received: 30.01.2004 Revised: 26.01.2006
Citation:
D. A. Shirobokov, “On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1074–1095; Comput. Math. Math. Phys., 46:6 (2006), 1023–1043
Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 1074--1095
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\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 1023--1043
\crossref{https://doi.org/10.1134/S0965542506060108}
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http://mi.mathnet.ru/eng/zvmmf460 http://mi.mathnet.ru/eng/zvmmf/v46/i6/p1074
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