Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik KRAUNC. Fiz.-Mat. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2023, Volume 45, Number 4, Pages 36–51
DOI: https://doi.org/10.26117/2079-6641-2023-45-4-36-51
(Mi vkam622)
 

MATHEMATICAL MODELING

Solution of the inverse problem of identifying the order of the fractional derivative in a mathematical model of the dynamics of solar activitythe at rising phase

D. A. Tvyordyj, R. I. Parovik

Institute for Cosmophysical Research and Radio Propagation FEB RAS
References:
Abstract: The article refines the mathematical model of solar activity dynamics by solving the inverse problem. Experimental data on the observation of Wolf number values are used as additional information. This parameter of solar activity reflects the number of spots on the surface of the sun, and is considered an indicator of its activity. This process is characterized by observable cyclicality, periods of growth and decline. The analysis and processing of the initial data is carried out in order to isolate from the time series areas corresponding to an increase in solar activity. To describe this dynamic process, a previously proposed mathematical model for describing cycles 23 and 24 is used. The model is a Cauchy problem for a fractional analogue of the nonlinear Riccati equation, where the first-order derivative is replaced by the Gerasimov-Caputo fractional differentiation operator with an order from 0 to 1. The order of the fractional derivative is associated with the intensity of the process. This model equation is solved numerically using a nonlocal implicit finite-difference scheme. To clarify the values of the order of the fractional derivative, the one-dimensional optimization problem was solved using the second-order Levenberg-Marquardt iterative method, based on processed experimental data. It is shown that it is possible to refine the order of the fractional derivative in the solar activity model by solving the corresponding inverse problem, and the results obtained are in better agreement with the data.
Keywords: mathematical modeling, reverse problem, solar activity, Wolf number, sunspots, dynamic processes, nonlinear equations, Riccati equation, saturation effect, fractional derivatives, ereditarity, MATLAB, C, parallel algorithms.
Funding agency Grant number
Russian Science Foundation 22-11-00064
The research was carried out within the framework of the Russian Science Foundation grant No. 22-11-00064 on the topic «Modeling of dynamic processes in the geospheres taking into account heredity».
Document Type: Article
UDC: 519.642.2
MSC: Primary 34A08; Secondary 34A34
Language: Russian
Citation: D. A. Tvyordyj, R. I. Parovik, “Solution of the inverse problem of identifying the order of the fractional derivative in a mathematical model of the dynamics of solar activitythe at rising phase”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 45:4 (2023), 36–51
Citation in format AMSBIB
\Bibitem{TvyPar23}
\by D.~A.~Tvyordyj, R.~I.~Parovik
\paper Solution of the inverse problem of identifying the order of the fractional derivative in a mathematical model of the dynamics of solar activitythe at rising phase
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 45
\issue 4
\pages 36--51
\mathnet{http://mi.mathnet.ru/vkam622}
\crossref{https://doi.org/10.26117/2079-6641-2023-45-4-36-51}
Linking options:
  • https://www.mathnet.ru/eng/vkam622
  • https://www.mathnet.ru/eng/vkam/v45/i4/p36
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
    Statistics & downloads:
    Abstract page:41
    Full-text PDF :20
    References:24
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024