This article is cited in 4 papers

Short Communication
Mathematical Modelling

On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives

V. D. Beybalaev

Daghestan State University, Makhachkala, Russia

Abstract: Difference approximation for the Caputo fractional derivative of the $4-\beta$, $1<\beta\leq 2$, order is obtained in the work. The difference schemes for solving the Dirichlet problem for the Poisson equation with fractional derivatives are developed. The right part and initial data stability of difference problem and its convergence are proved.

Keywords: Poisson's equation, Dirichlet problem, fractional order derivative, numerical method, approximation, difference problem.

UDC: 519.642.2:517.968.72

MSC: Primary 39A14; Secondary 35R11, 26A33, 45K05

Original article submitted 22/IV/2011
revision submitted – 12/XII/2011

DOI: 10.14498/vsgtu946

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