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Izv. IMI UdGU, 2021, Volume 57, Pages 156–169 (Mi iimi414)  

MATHEMATICS

Numerical method for fractional diffusion-wave equations with functional delay

V. G. Pimenov, E. E. Tashirova

Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia

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.

Keywords: fractional diffusion wave equation, functional delay, L2-method, interpolation, Crank-Nicholson scheme, order of convergence.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00019
The study funded by RFBR, project number 19-01-00019.


DOI: https://doi.org/10.35634/2226-3594-2021-57-07

Full text: PDF file (170 kB)
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Bibliographic databases:

UDC: 519.63
MSC: 65M06, 65M12, 65M15, 65Q20
Received: 04.03.2021

Citation: V. G. Pimenov, E. E. Tashirova, “Numerical method for fractional diffusion-wave equations with functional delay”, Izv. IMI UdGU, 57 (2021), 156–169

Citation in format AMSBIB
\Bibitem{PimTas21}
\by V.~G.~Pimenov, E.~E.~Tashirova
\paper Numerical method for fractional diffusion-wave equations with functional delay
\jour Izv. IMI UdGU
\yr 2021
\vol 57
\pages 156--169
\mathnet{http://mi.mathnet.ru/iimi414}
\crossref{https://doi.org/10.35634/2226-3594-2021-57-07}


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