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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 52

Convergence of the High Accuracy Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay

Author(s)
Vladimir G. Pimenov1, Andrei V. Lekomtsev1

1Ural Federal University, Yekaterinburg, Russian Federation

Abstract
In this paper, the nonlinear superdiffusion equation with functional delay is considered. The discretization of the problem is performed. Constructions of the high accuracy difference method with piecewise linear interpolation are given. The order of the residual of the numerical method is studied. Under certain assumptions, the convergence of the second order in spatial and temporal steps and stability of the method is proved. The results of numerical experiments on test examples are presented.
About the Authors

Vladimir G. Pimenov, Dr. Sci. (Phys.–Math.), Prof., Ural Federal University, Yekaterinburg, 620075, Russian Federation, v.g.pimenov@urfu.ru

Andrei V. Lekomtsev, Cand. Sci. (Phys.Math.), Ural Federal University, Yekaterinburg, 620075, Russian Federation, avlekomtsev@urfu.ru

For citation
Pimenov V. G., Lekomtsev A. V. Convergence of the High Accuracy Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 52, pp. 105–119. (in Russian)

https://doi.org/10.26516/1997-7670.2025.52.105

Keywords
nonlinear superdiffusion equation, functional delay, piecewise linear interpolation, higher order of convergence, quasilinearity
UDC
519.633
MSC
65N06, 34A08
DOI
https://doi.org/10.26516/1997-7670.2025.52.105
References
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