Numerical Method of Solution of the Problem on Transposition of Two-sided Derivative of the Fractional Order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2009), pp. 267-270.

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Numerical method of the solution of the problem of heat transposition with two-sided derivative of the fractional order along the space variable and with the fractional order derivative in time is studied. Finite-different scheme was constructed and the stability of this different scheme was proven.
Keywords: numerical methods, approximation, differential equations, stability.
Mots-clés : fractal, fractal structure
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V. D. Beybalaev. Numerical Method of Solution of the Problem on Transposition of Two-sided Derivative of the Fractional Order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2009), pp. 267-270. http://geodesic.mathdoc.fr/item/VSGTU_2009_1_a29/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Mn., 1987, 688 pp. | MR | Zbl

[2] Nakhushev A. M., Elementy drobnogo ischisleniya i ikh primenenie, KB NTs RAN, Nalchik, 2000, 299 pp.

[3] Goloviznin V. M., Kiselev V. P., Korotkin I. A., Yurko Yu. I., “Pryamye zadachi neklassicheskogo perenosa radionuklidov v geologicheskikh formatsiyakh”, Izvest. RAN. Energetika, 2004, no. 4, 121–130

[4] Isaacson E., Keller H. B., Analysis of Numerical Methods, Wiley Sons, Inc., New York – London – Sydney, 1966, 541 pp. | MR | Zbl

[5] Beibalaev V. D., “Chislennyi metod resheniya matematicheskoi modeli teploperenosa v sredakh s fraktalnoi strukturoi”, Fundamentalnye issledovaniya, 2007, no. 12, 249–251

[6] Tadjeran Charles, Meerschaert Mark M., Scheffler Hana–Peter, “A second-order accurate numerical approximation for the fractional diffusion equation”, J. Computat. Phys., 213:1 (2006), 205–213 | DOI | MR | Zbl

[7] Liu Q., Liu F., Turner I., Anh V., “Approximation of the Levy–Feller advection-dispersion process by random walk and finite difference method”, J. Computat. Phys., 222:1 (2007), 57–70 | DOI | MR | Zbl

[8] Goloviznin V. M., Kiselev V. P., Korotkin I. A., Chislennye metody resheniya uravneniya drobnoi diffuzii v odnomernom sluchae, Preprint No IBRAE–2002–10, IBRAE RAN, M., 2002, 35 pp.