A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind

Anatoly A. Alikhanov; Inna Z. Kodzokova

doi:10.1007/978-3-319-57099-0_15

A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind

Anatoly A. Alikhanov^*
, Inna Z. Kodzokova

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters α, β and γ. Weobtaina prioriesti-mates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.

Original language	English
Title of host publication	Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers
Editors	Ivan Dimov, Istvan Farago, Lubin Vulkov
Publisher	Springer Verlag
Pages	164-171
Number of pages	8
ISBN (Print)	9783319570983
DOIs	https://doi.org/10.1007/978-3-319-57099-0_15
State	Published - 2017
Externally published	Yes
Event	6th International Conference on Numerical Analysis and Its Applications, NAA 2016 - Lozenetz, Bulgaria Duration: 15 Jun 2016 → 22 Jun 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10187 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th International Conference on Numerical Analysis and Its Applications, NAA 2016
Country/Territory	Bulgaria
City	Lozenetz
Period	15/06/16 → 22/06/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-57099-0_15

Cite this

Alikhanov, A. A., & Kodzokova, I. Z. (2017). A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind. In I. Dimov, I. Farago, & L. Vulkov (Eds.), Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers (pp. 164-171). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-57099-0_15

Alikhanov, Anatoly A. ; Kodzokova, Inna Z. / A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind. Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers. editor / Ivan Dimov ; Istvan Farago ; Lubin Vulkov. Springer Verlag, 2017. pp. 164-171 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind",

abstract = "We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters α, β and γ. Weobtaina prioriesti-mates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.",

author = "Alikhanov, \{Anatoly A.\} and Kodzokova, \{Inna Z.\}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 6th International Conference on Numerical Analysis and Its Applications, NAA 2016 ; Conference date: 15-06-2016 Through 22-06-2016",

year = "2017",

doi = "10.1007/978-3-319-57099-0\_15",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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booktitle = "Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers",

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Alikhanov, AA & Kodzokova, IZ 2017, A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind. in I Dimov, I Farago & L Vulkov (eds), Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10187 LNCS, Springer Verlag, pp. 164-171, 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, Lozenetz, Bulgaria, 15/06/16. https://doi.org/10.1007/978-3-319-57099-0_15

A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind. / Alikhanov, Anatoly A.; Kodzokova, Inna Z.
Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers. ed. / Ivan Dimov; Istvan Farago; Lubin Vulkov. Springer Verlag, 2017. p. 164-171 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10187 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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PY - 2017

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N2 - We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters α, β and γ. Weobtaina prioriesti-mates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.

AB - We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters α, β and γ. Weobtaina prioriesti-mates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers

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Alikhanov AA, Kodzokova IZ. A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind. In Dimov I, Farago I, Vulkov L, editors, Numerical Analysis and Its Applications - 6th International Conference, NAA 2016, Revised Selected Papers. Springer Verlag. 2017. p. 164-171. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-57099-0_15

A higher order difference scheme for the time fractional diffusion equation with the Steklov nonlocal boundary value problem of the second kind

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

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Cite this