Geodesic
A linearized difference scheme for a class of fractional partial differential equations with delay
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2015), pp. 236-242 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A class of non linear fractional partial differential equations with initial and Dirichlet boundary conditions is under consideration. We seek to obtain numerical solutions for this considered class of equations based on finite difference method. The convergence order will be $2-\alpha$ in time and four in space. A numerical example is given to support the theoretical results.
Keywords: fractional partial differential equation, linear difference scheme, delay, discrete energy method, convergence analysis. 
@article{IIMI_2015_2_a28,
     author = {A. S. Hendy},
     title = {A linearized difference scheme for a class of fractional partial differential equations with delay},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {236--242},
     year = {2015},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_2_a28/}
}
TY  - JOUR
AU  - A. S. Hendy
TI  - A linearized difference scheme for a class of fractional partial differential equations with delay
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2015
SP  - 236
EP  - 242
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IIMI_2015_2_a28/
LA  - en
ID  - IIMI_2015_2_a28
ER  - 
%0 Journal Article
%A A. S. Hendy
%T A linearized difference scheme for a class of fractional partial differential equations with delay
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2015
%P 236-242
%N 2
%U http://geodesic.mathdoc.fr/item/IIMI_2015_2_a28/
%G en
%F IIMI_2015_2_a28
A. S. Hendy. A linearized difference scheme for a class of fractional partial differential equations with delay. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2015), pp. 236-242. http://geodesic.mathdoc.fr/item/IIMI_2015_2_a28/

[1] Ferreira J., “Energy estimates for delay diffusion-reaction equations”, J. Comp. Math., 26:4 (2008), 536–553 | MR | Zbl

[2] Hao Z., Sun Z., Cao W., “A fourth order approximation of fractional derivatives with its applications”, J. Comp. Phys., 281 (2015), 787–805 | DOI | MR

[3] Karatay I., Kale N., Bayramoglu S., “A new difference scheme for time fractional heat equations based on Crank–Nicolson method”, Fract. Calc. Appl. Anal., 16:4 (2013), 893–910 | DOI | MR

[4] Khader M. M., El Danaf T. S., Hendy S. A., “A computational matrix method for solving systems of high order fractional differential equations”, Appl. Math. Model., 37 (2013), 4035–4050 | DOI | MR | Zbl

[5] Pimenov G. V., Hendy S. A., “Numerical studies for fractional functional differential equations with delay based on BDF-Type shifted Chebyshev polynomials”, Abstract and Applied Analysis, 2015 (2015), article ID 510875 | DOI | MR

[6] Zhang Y., “A finite difference method for fractional partial differential equation”, Appl. Math. Comp., 16:2 (2009), 524–529 | DOI | MR

[7] Zhang Z., Sun Z., “A linearized compact difference scheme for a class of nonlinear delay partial differential equations”, Appl. Math. Model., 37:3 (2013), 742–752 | DOI | MR