Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102812
Title: Numerical method for fractional diffusion-wave equations with functional delay
ЧИСЛЕННЫЙ МЕТОД ДЛЯ ДРОБНЫХ ДИФФУЗИОННО-ВОЛНОВЫХ УРАВНЕНИЙ С ФУНКЦИОНАЛЬНЫМ ЗАПАЗДЫВАНИЕМ
Authors: Germanovich, P. V.
Evgen'evna, T. E.
Issue Date: 2021
Publisher: Udmurt State University
Citation: Germanovich P. V. Numerical method for fractional diffusion-wave equations with functional delay / P. V. Germanovich, T. E. Evgen'evna. — DOI 10.35634/2226-3594-2021-57-07 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2021. — Vol. 57. — P. 156-169.
Abstract: For a fractional diffusion-wave equation with a nonlinear effect of functional delay, an implicit numerical method is constructed. The scheme is based on the L2-method of approximation of the fractional derivative of the order from 1 to 2, interpolation and extrapolation with the given properties of discrete prehistory and an analogue of the Crank-Nicolson method. The order of convergence of the method is investigated using the ideas of the general theory of difference schemes with heredity. The order of convergence of the method is more significant than in previously known methods, depending on the order of the starting values. The main point of the proof is the use of the stability of the L2-method. The results of comparing numerical experiments with other schemes are presented: A purely implicit method and a purely explicit method, these results showed, in general, the advantages of the proposed scheme. © 2021 Udmurt State University. All rights reserved.
Keywords: CRANK- NICHOLSON SCHEME
FRACTIONAL DIFFUSION WAVE EQUATION
FUNCTIONAL DELAY
INTERPOLATION
L2-METHOD
ORDER OF CONVERGENCE
URI: http://hdl.handle.net/10995/102812
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85108965043
PURE ID: 22131821
ISSN: 22263594
DOI: 10.35634/2226-3594-2021-57-07
metadata.dc.description.sponsorship: The study funded by RFBR, project number 19–01–00019.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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