Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/111955
Title: An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay
Authors: Omran, A. K.
Zaky, M. A.
Hendy, A. S.
Pimenov, V. G.
Issue Date: 2021
Publisher: Hindawi Limited
Hindawi Limited
Citation: An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay / A. K. Omran, M. A. Zaky, A. S. Hendy et al. // Journal of Function Spaces. — 2021. — Vol. 2021. — 5922853.
Abstract: In this paper, we construct and analyze a linearized finite difference/Galerkin-Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0<β0<β1<β2<⋯<βm<1. The problem is first approximated by the L1 difference method on the temporal direction, and then, the Galerkin-Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2-βm in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results. © 2021 A. K. Omran et al.
URI: http://elar.urfu.ru/handle/10995/111955
Access: info:eu-repo/semantics/openAccess
RSCI ID: 47551986
SCOPUS ID: 85122268250
WOS ID: 000739418400001
PURE ID: 29376427
ISSN: 2314-8896
DOI: 10.1155/2021/5922853
metadata.dc.description.sponsorship: A. K. Omran is funded by a scholarship under the joint executive program between the Arab Republic of Egypt and Russian Federation. M. A. Zaky wishes to acknowledge the support of the Nazarbayev University Program (091019CRP2120). M. A. Zaky wishes also to acknowledge the partial support of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant “Dynamical Analysis and Synchronization of Complex Neural Networks with Its Applications”).
Appears in Collections:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

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