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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 10, Pages 1604–1615 (Mi zvmmf10788)  

Numerical solution of time-dependent problems with different time scales

P. N. Vabishchevichab, P. E. Zakharovb

a Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia
b Ammosov North-Eastern Federal University, Yakutsk, Russia

Abstract: Problems for time-dependent equations in which processes are characterized by different time scales are studied. Parts of the equations describing fast and slow processes are distinguished. The basic features of such problems related to their approximation are taken into account using finer time grids for fast processes. The construction and analysis of inhomogeneous time approximations is based on the theory of additive operator-difference schemes (splitting schemes). To solve time-dependent problems with different time scales, componentwise splitting schemes and vector additive schemes are used. The capabilities of the proposed schemes are illustrated by numerical examples for the time-dependent convection-diffusion problem. If convection is dominant, the convective transfer is computed on a finer time grid.

Key words: non-uniformly scaled problems, inhomogeneous finite difference schemes, splitting schemes, convection-diffusion problems.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0013


DOI: https://doi.org/10.31857/S004446690003581-0

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:10, 1552–1561

Bibliographic databases:

UDC: 519.633
Received: 18.08.2017

Citation: P. N. Vabishchevich, P. E. Zakharov, “Numerical solution of time-dependent problems with different time scales”, Zh. Vychisl. Mat. Mat. Fiz., 58:10 (2018), 1604–1615; Comput. Math. Math. Phys., 58:10 (2018), 1552–1561

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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