Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Editorial staff
Guidelines for authors
License agreement
Editorial policy

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 3, Pages 582–597 (Mi vsgtu1690)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communication

Stability and convergence of difference schemes for the multi-term time-fractional diffusion equation with generalized memory kernels

A. Kh. Khibiev

Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS, Nal’chik, 360000, Russian Federation.

Abstract: In this paper, a priori estimate for the corresponding differential problem is obtained by using the method of the energy inequalities. We construct a difference analog of the multi-term Caputo fractional derivative with generalized memory kernels (analog of L1 formula). The basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the $ (2{-}\alpha_0) $-th order in time for the generalized multi-term time-fractional diffusion equation with variable coefficients are considered. Stability of the suggested schemes and also their convergence in the grid $ L_2 $-norm with the rate equal to the order of the approximation error are proved. The obtained results are supported by numerical calculations carried out for some test problems.

Keywords: fractional derivative, generalized memory kernel, a priori estimates, fractional diffusion equation, finite difference scheme, stability, convergence

DOI: https://doi.org/10.14498/vsgtu1690

Full text: PDF file (1066 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 519.642.2
MSC: 65M06, 65N06, 65N12
Received: April 16, 2019
Revised: May 25, 2019
Accepted: June 10, 2019
First online: June 21, 2019

Citation: A. Kh. Khibiev, “Stability and convergence of difference schemes for the multi-term time-fractional diffusion equation with generalized memory kernels”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:3 (2019), 582–597

Citation in format AMSBIB
\Bibitem{Khi19}
\by A.~Kh.~Khibiev
\paper Stability and convergence of difference schemes for~the~multi-term time-fractional diffusion equation with~generalized memory kernels
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 3
\pages 582--597
\mathnet{http://mi.mathnet.ru/vsgtu1690}
\crossref{https://doi.org/10.14498/vsgtu1690}


Linking options:
  • http://mi.mathnet.ru/eng/vsgtu1690
  • http://mi.mathnet.ru/eng/vsgtu/v223/i3/p582

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Kh. Beshtokov, “Kraevye zadachi dlya nagruzhennogo modifitsirovannogo uravneniya vlagoperenosa drobnogo poryadka s operatorom Besselya i raznostnye metody ikh resheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 158–175  mathnet  crossref
    2. Gu X.-M., Huang T.-Zh., Zhao Y.-L., Lyu P., Carpentieri B., “a Fast Implicit Difference Scheme For Solving the Generalized Time-Space Fractional Diffusion Equations With Variable Coefficients”, Numer. Meth. Part Differ. Equ., 37:2 (2021), 1136–1162  crossref  mathscinet  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
    Number of views:
    This page:319
    Full text:164
    References:25

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021