Geodesic
Implicit and efficient schemes for a parabolic equation in a spherical layer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 605-614 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Implicit and efficient schemes for a~parabolic equation in a~spherical layer},
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E. I. Aksenova. Implicit and efficient schemes for a parabolic equation in a spherical layer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 605-614. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a5/

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