Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type
V.A. Litvinov1, V.V. Uchaikin2
1Barnaul Law Institute of the Ministry of Internal Affairs of Russia, Barnaul, Russia
2Ulyanovsk State University, Ulyanovsk, Russia
Keywords: inverse problems, diffusion equation, operators, fractional derivatives
Abstract
The work considers problem of reconstruction of differential equations parameters, describing anomalous diffusion processes, on the base of known solutions. As a tool, is used the variational interpolation method elaborated by the authors earlier. The reconstruction time-dependence of diffusivity and determination of fractional time- and space-derivatives order in anomalous diffusion equation is demonstrated. There is shown a possibility of sufficient accuracy with insignificant computational expanses.
|
