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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 605–614 (Mi zvmmf483)  

Implicit and efficient schemes for a parabolic equation in a spherical layer

E. I. Aksenova

Moscow Mezhregion Bar, Poluyaroslavskii per. 3/5, Moscow, 105120, Russia

Abstract: An implicit and an efficient three-level scheme for a parabolic equation in spherical coordinates is constructed in a spherical layer. No axial symmetry is assumed. The convergence rates of the schemes are estimated under minimum requirements on the initial data. The estimates are uniform with respect to the inner diameter of the domain. The order of convergence is $\tau^{\alpha/2}+h^\alpha$, $\alpha=1,2$, depending on the smoothness of the data. The results remain valid for a domain without a hole.

Key words: parabolic boundary value problems, spherical coordinates, domain with a small hole, three-level efficient difference scheme, convergence rate estimate.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 575–584

Bibliographic databases:

UDC: 519.633.6
Received: 30.06.2004
Revised: 21.03.2005

Citation: E. I. Aksenova, “Implicit and efficient schemes for a parabolic equation in a spherical layer”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 605–614; Comput. Math. Math. Phys., 46:4 (2006), 575–584

Citation in format AMSBIB
\Bibitem{Aks06}
\by E.~I.~Aksenova
\paper Implicit and efficient schemes for a~parabolic equation in a~spherical layer
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 605--614
\mathnet{http://mi.mathnet.ru/zvmmf483}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260352}
\zmath{https://zbmath.org/?q=an:05200931}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 575--584
\crossref{https://doi.org/10.1134/S0965542506040063}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746069650}


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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