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Efficient three-level scheme for parabolic equations in cylindrical coordinates in a region with a small hole

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Abstract

An efficient three-level scheme for parabolic equations in cylindrical coordinates is constructed in a region with a small hole. No axial symmetry is assumed. The convergence rate of the scheme is estimated under minimum requirements on the initial data. The estimates are uniform with respect to a small parameter—the inner diameter of the region. The order of convergence is τ + h 2, τ1/2 + h, τ + h, depending on the smoothness of the data.

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

    E. I. Aksenova

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  1. E. I. Aksenova
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Original Russian Text © E.I. Aksenova, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 445–456.

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Aksenova, E.I. Efficient three-level scheme for parabolic equations in cylindrical coordinates in a region with a small hole. Comput. Math. and Math. Phys. 46, 425–436 (2006). https://doi.org/10.1134/S0965542506030092

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  • DOI: https://doi.org/10.1134/S0965542506030092

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