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.
Citation:
V. D. Beybalaev, “On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(27) (2012), 183–187
\Bibitem{Bey12}
\by V.~D.~Beybalaev
\paper On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 2(27)
\pages 183--187
\mathnet{http://mi.mathnet.ru/vsgtu946}
\crossref{https://doi.org/10.14498/vsgtu946}
\zmath{https://zbmath.org/?q=an:1326.39007}
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https://www.mathnet.ru/eng/vsgtu946
https://www.mathnet.ru/eng/vsgtu/v127/p183
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