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 Izv. IMI UdGU, 2021, Volume 57, Pages 91–103 (Mi iimi410)

MATHEMATICS

Numerical algorithm for fractional order population dynamics model with delay

T. V. Gorbova

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

Abstract: For a fractional-diffusion equation with nonlinearity in the differentiation operator and with the effect of functional delay, an implicit numerical method is constructed based on the approximation of the fractional derivative and the use of interpolation and extrapolation of discrete history. The source of this problem is a generalized model from population theory. Using a fractional discrete analogue of Gronwall's lemma, the convergence of the method is proved under certain conditions. The resulting system of nonlinear equations using Newton's method is reduced to a sequence of linear systems with tridiagonal matrices. Numerical results are given for a test example with distributed delay and a model example from the theory of population with concentrated constant delay.

Keywords: population model, fractional-diffusion equation, differentiation with nonlinearity, functional delay, difference scheme, Newton's method, order of convergence.

DOI: https://doi.org/10.35634/2226-3594-2021-57-03

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Bibliographic databases:

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

Citation: T. V. Gorbova, “Numerical algorithm for fractional order population dynamics model with delay”, Izv. IMI UdGU, 57 (2021), 91–103

Citation in format AMSBIB
\Bibitem{Gor21} \by T.~V.~Gorbova \paper Numerical algorithm for fractional order population dynamics model with delay \jour Izv. IMI UdGU \yr 2021 \vol 57 \pages 91--103 \mathnet{http://mi.mathnet.ru/iimi410} \crossref{https://doi.org/10.35634/2226-3594-2021-57-03}