Algorithms of numerical solution of fractional differential equations

Аuthors

Petukhov A. A.^*, Reviznikov D. L.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: petuhov-anton@yandex.ru
**e-mail: reviznikov@inbox.ru

Abstract

Some problems of numerical solution of fractional differential equations for anomalous diffusion are considered. Numerical algorithms are presented for the equation with fractional derivatives in time and space. Analysis of stability and approximation is carried out for developed explicit and implicit schemes. It is shown that the numerical results are in good agreement with exact analytical solution.

Keywords:

fractional derivative, anomalous diffusion, difference scheme, computational algorithm, Grunevald-Letnikov formula