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On the multioperator method for constructing approximations and finite difference schemes of an arbitrarily high order

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Abstract

Main results of the development of the multioperator method for constructing approximations of prescribed order are presented. Multioperators for various approximation problems are considered. The focus is on the multioperators for convective terms in fluid dynamics equations. Types of multioperator schemes are described and possibilities for their optimization are discussed. Results of solving benchmark problems in the case of tenth- and 18th-order schemes are presented.

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    A. I. Tolstykh

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  1. A. I. Tolstykh
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Correspondence to A. I. Tolstykh.

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Dedicated to Academician A.A. Dorodnicyn on the Occasion of the Centenary of His Birth

Original Russian Text © A.I. Tolstykh, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 1, pp. 56–73.

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Tolstykh, A.I. On the multioperator method for constructing approximations and finite difference schemes of an arbitrarily high order. Comput. Math. and Math. Phys. 51, 51–67 (2011). https://doi.org/10.1134/S0965542511010131

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