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 Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 1074–1095 (Mi zvmmf460)

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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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 1023–1043

Bibliographic databases:

UDC: 519.634
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
\Bibitem{Shi06} \by D.~A.~Shirobokov \paper On the construction of second-to-fourth-order accurate approximations of spatial derivatives on an arbitrary set of points \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2006 \vol 46 \issue 6 \pages 1074--1095 \mathnet{http://mi.mathnet.ru/zvmmf460} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285366} \transl \jour Comput. Math. Math. Phys. \yr 2006 \vol 46 \issue 6 \pages 1023--1043 \crossref{https://doi.org/10.1134/S0965542506060108} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746136013}