IKBFU's Vestnik

2010 Issue №4

Optimal parameters for consequences of tangential and two-frequency decompositions

Abstract

A preconditioner for large systems of linear equations based on an incomplete block-decomposition for a block-tridiagonal matrices is considered. This method generalizes methods are developed by Buzdin and Wittum [1; 2]. A method of choosing quasioptimal parameters for consequences of tangential and two-frequencies decompositions based on analysis of model problems is developed. It’s convergence rate is better than ADI’s convergence rate in commutational case..

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An mathematical simulation of ionosphere with due regard for its three-dimensional irregularity

Abstract

Difference methods an approximate solution of a three-dimensional equation of ions diffusion with mixed derivatives and divergence first derivatives are considered. The task is reduced to a chain of three two-dimensional parabolic equations on base of the summary approximation method. Difference operators are constructed, and an analysis of its properties, test calculations and an estimate of a mixed derivatives role are carried out.

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A semicanonical normal affine connection associated with the distribution

Abstract

In manydimensional projective space distribution of planes is considered. The way of giving normal generalized affine connection associated with the distribution is proposed. It is shown that this connection is given by connection tensor and normal linear connection object. They define its curvature and torsion tensors. Semicanonical case is investigated when subtensor of the connection tensor vanishes. Two notions are
involved: non-degeneration tensor of torsion and semiholonomical distribution. It is proved that vanishing of non-degeneration tensor implies degenerating to linear connection of the semicanonical normal affine connection. The notion of semiholonomity let us describe semicanonical connection without torsion with non-zero nondegeneration tensor.

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