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Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation

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Abstract

A family of difference schemes for the fractional-order diffusion equation with variable coefficients is considered. By the method of energetic inequalities, a priori estimates are obtained for solutions of finite-difference problems, which imply the stability and convergence of the difference schemes considered. The validity of the results is confirmed by numerical calculations for test examples.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, ul. Shortanova 89-A, Nalchik, 360000, Russia

    A. A. Alikhanov

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  1. A. A. Alikhanov
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Correspondence to A. A. Alikhanov.

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Original Russian Text © A.A. Alikhanov, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 4, pp. 572–586.

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Alikhanov, A.A. Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation. Comput. Math. and Math. Phys. 56, 561–575 (2016). https://doi.org/10.1134/S0965542516040035

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  • DOI: https://doi.org/10.1134/S0965542516040035

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