Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

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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.

Keywords

evolution equation elliptic operator fractional-power operator two-level difference schemes 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Nuclear Safety InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Ammosov North-Eastern Federal UniversityYakutskRussia

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