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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 414–430 (Mi zvmmf10693)  

Numerical solution of time-dependent problems with a fractional-power elliptic operator

P. N. Vabishchevichab

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

Abstract: A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Key words: evolution equation, elliptic operator, fractional-power operator, two-level difference schemes.

Funding Agency Grant Number
Bulgarian National Science Fund DN 12/1
Russian Foundation for Basic Research 17-51-53008_ГФЕН_а


DOI: https://doi.org/10.7868/S0044466918030092

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 394–409

Bibliographic databases:

UDC: 519.633
Received: 01.06.2016

Citation: P. N. Vabishchevich, “Numerical solution of time-dependent problems with a fractional-power elliptic operator”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 414–430; Comput. Math. Math. Phys., 58:3 (2018), 394–409

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