### Numerical solution of the boundary value problem for the heat equation with fractional Riesz derivative

Vetlugin Beybalayev, Abutrab Aliverdiev

Article ID: 2082
Vol 6, Issue 2, 2023

VIEWS - 197 (Abstract) 125 (PDF)

#### Abstract

The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

#### Keywords

fractional Riesz derivative; difference scheme; approximation; convergence; thermal transport

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DOI: https://doi.org/10.24294/tse.v6i2.2082

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