Mots-clés : Interpolation, Extrapolation, Convergence order.
@article{UMJ_2016_2_1_a4,
author = {Vladimir G. Pimenov and Ahmed S. Hendy},
title = {Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay},
journal = {Ural mathematical journal},
pages = {48--57},
year = {2016},
volume = {2},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/}
}
TY - JOUR AU - Vladimir G. Pimenov AU - Ahmed S. Hendy TI - Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay JO - Ural mathematical journal PY - 2016 SP - 48 EP - 57 VL - 2 IS - 1 UR - http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/ LA - en ID - UMJ_2016_2_1_a4 ER -
%0 Journal Article %A Vladimir G. Pimenov %A Ahmed S. Hendy %T Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay %J Ural mathematical journal %D 2016 %P 48-57 %V 2 %N 1 %U http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/ %G en %F UMJ_2016_2_1_a4
Vladimir G. Pimenov; Ahmed S. Hendy. Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay. Ural mathematical journal, Tome 2 (2016) no. 1, pp. 48-57. http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/
[1] Wu J., Theory and applications of partial functional differential equations, Springer-Verlag, New York, 1996, 438 pp.
[2] Zhang B., Zhou Y., Qualitative analysis of delay partial difference equations, Hindawi Publishing Corporation, New York, 2007, 375 pp.
[3] Tavernini L., “Finite difference approximations for a class of semilinear Volterra evolution problems”, SIAM J. Numer. Anal., 14:5 (1977), 931–949
[4] Van Der Houwen P.J., Sommeijer B.P., Baker C.T.H., “On the stability of predictor-corrector methods for parabolic equations with delay”, IMA J. Numer. Anal., 6 (1986), 1–23
[5] Zubik-Kowal B., “The method of lines for parabolic differential-functional equations”, IMA J. Numer. Anal., 17 (1997), 103–123
[6] Kropielnicka K., “Convergence of Implicit Difference Methods for Parabolic Functional Differential Equations”, Int. Journal of Mat. Analysis, 1:6 (2007), 257–277
[7] Garcia P., Castro M.A., Martin J.A., Sirvent A., “Convergence of two implicit numerical schemes for diffusion mathematical models with delay”, Mathematical and Computer Modelling, 52 (2010), 1279–1287
[8] Pimenov V.G., Lozhnikov A.B., “Difference schemes for the numerical solution of the heat conduction equation with aftereffect”, Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S137–S148 | DOI
[9] Samarskii A.A., Theory of difference schemes, Nauka, Moscow, 1989, 656 pp. (in Russian)
[10] Pimenov V.G., “General linear methods for the numerical solution of functional-differential equations”, Differ. Equ., 37:1 (2001), 116–127 | DOI
[11] Kim A.V., Pimenov V.G., i-smooth calculus and numerical methods for functional differential equations, Regular and Chaotic Dynamics, Moscow–Izhevsk, 2004, 256 pp. (in Russian)
[12] Pimenov V.G., Tashirova E.E., “Numerical methods for solving a hereditary equation of hyperbolic type”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 126–136 | DOI
[13] Lekomtsev A.V., Pimenov V.G., “Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S101–S118 | DOI
[14] Lekomtsev A, Pimenov V., “Convergence of the scheme with weights for the numerical solution of a heat conduction equation with delay for the case of variable coefficient of heat conductivity”, Appl.Math.Comput., 256 (2015), 83–93
[15] Pimenov V.G., Difference methods for the solution of the equations in partial derivatives with heredity, Ural Federal University, Ekaterinburg, 2014, 232 pp. (in Russian)
[16] Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives: Theory and Applications, CRC Press, Boca Raton, 1993, 1006 pp.
[17] Miller K, Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993, 384 pp.
[18] Podlubny I., Fractional differential equations, Acad. Press, San Diego, 1999, 368 pp.
[19] Khader M.M., Danaf T.E., Hendy A.S., “A computational matrix method for solving systems of high order fractional differential equations”, Appl. Math. Modell., 37:6 (2013), 4035–4050
[20] Pimenov V., Hendy V., “Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations”, Article ID 510875, Abstract and Applied Analysis, 2015, 1–12
[21] Alikhanov A.A., “Numerical methods of solutions boundary value problems for multi-term veriable-distributed order diffusion equations”, Appl.Math.Comput., 268 (2015), 12–22
[22] Meerschaert M.M., Tadjeran C., “Finite difference approximations for two sided space fractional partial differential equations”, Applied numerical mathematics, 65 (2006), 80–90
[23] Tadjeran C., Meerschaert M.M., Scheffler H.P., “A second-order accurate numerical approximation for the fractional diffusion equation”, J. of Computational Physics, 213 (2006), 205–214
[24] Pimenov V.G., Hendy A.S., “Numerical methods for the equation with fractional derivative on state and with functional delay on time”, Bulletin of the Tambov university. Natural and technical science, 20:5 (2015), 1358–1361
[25] Wang H., Wang K., Sircar T., “A direct O(Nlog2N) finite difference method for fractional diffusion equations”, J. of Computational Physics, 229 (2010), 8095–8104
[26] Isaacson E., Keller H.B., Analysis of Numerical Methods, Wiley, New York, 1966, 541 pp.