A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders

A. Alikhanov; A. Apekov; C. Huang

doi:10.1007/978-3-030-97020-8_47

A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders

A. Alikhanov^*
, A. Apekov
, C. Huang

^*Corresponding author for this work

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

3 Scopus citations

Abstract

A difference schemes of a higher order of approximation for the time-fractional diffusion equation of multi-term and distributed orders are constructed on the basis of the L2 type formula. The stability and convergence of the proposed difference schemes is proved by the method of energy inequalities.

Original language	English
Title of host publication	Mathematics and its Applications in New Computer Systems - MANCS 2021
Editors	Andrei Tchernykh, Anatoly Alikhanov, Mikhail Babenko, Irina Samoylenko
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	515-523
Number of pages	9
ISBN (Print)	9783030970192
DOIs	https://doi.org/10.1007/978-3-030-97020-8_47
State	Published - 2022
Externally published	Yes
Event	International Conference on Mathematics and its Applications in New Computer Systems, MANCS 2021 - Stavropol, Russian Federation Duration: 15 Dec 2021 → 17 Dec 2021

Publication series

Name	Lecture Notes in Networks and Systems
Volume	424
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	International Conference on Mathematics and its Applications in New Computer Systems, MANCS 2021
Country/Territory	Russian Federation
City	Stavropol
Period	15/12/21 → 17/12/21

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Convergence
Finite difference method
Stability
Time-fractional diffusion equation

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications

Access to Document

10.1007/978-3-030-97020-8_47

Cite this

Alikhanov, A., Apekov, A., & Huang, C. (2022). A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders. In A. Tchernykh, A. Alikhanov, M. Babenko, & I. Samoylenko (Eds.), Mathematics and its Applications in New Computer Systems - MANCS 2021 (pp. 515-523). (Lecture Notes in Networks and Systems; Vol. 424). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-97020-8_47

Alikhanov, A. ; Apekov, A. ; Huang, C. / A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders. Mathematics and its Applications in New Computer Systems - MANCS 2021. editor / Andrei Tchernykh ; Anatoly Alikhanov ; Mikhail Babenko ; Irina Samoylenko. Springer Science and Business Media Deutschland GmbH, 2022. pp. 515-523 (Lecture Notes in Networks and Systems).

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abstract = "A difference schemes of a higher order of approximation for the time-fractional diffusion equation of multi-term and distributed orders are constructed on the basis of the L2 type formula. The stability and convergence of the proposed difference schemes is proved by the method of energy inequalities.",

keywords = "Convergence, Finite difference method, Stability, Time-fractional diffusion equation",

author = "A. Alikhanov and A. Apekov and C. Huang",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; International Conference on Mathematics and its Applications in New Computer Systems, MANCS 2021 ; Conference date: 15-12-2021 Through 17-12-2021",

year = "2022",

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Alikhanov, A, Apekov, A & Huang, C 2022, A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders. in A Tchernykh, A Alikhanov, M Babenko & I Samoylenko (eds), Mathematics and its Applications in New Computer Systems - MANCS 2021. Lecture Notes in Networks and Systems, vol. 424, Springer Science and Business Media Deutschland GmbH, pp. 515-523, International Conference on Mathematics and its Applications in New Computer Systems, MANCS 2021, Stavropol, Russian Federation, 15/12/21. https://doi.org/10.1007/978-3-030-97020-8_47

A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders. / Alikhanov, A.; Apekov, A.; Huang, C.
Mathematics and its Applications in New Computer Systems - MANCS 2021. ed. / Andrei Tchernykh; Anatoly Alikhanov; Mikhail Babenko; Irina Samoylenko. Springer Science and Business Media Deutschland GmbH, 2022. p. 515-523 (Lecture Notes in Networks and Systems; Vol. 424).

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

TY - GEN

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AU - Alikhanov, A.

AU - Apekov, A.

AU - Huang, C.

PY - 2022

Y1 - 2022

N2 - A difference schemes of a higher order of approximation for the time-fractional diffusion equation of multi-term and distributed orders are constructed on the basis of the L2 type formula. The stability and convergence of the proposed difference schemes is proved by the method of energy inequalities.

AB - A difference schemes of a higher order of approximation for the time-fractional diffusion equation of multi-term and distributed orders are constructed on the basis of the L2 type formula. The stability and convergence of the proposed difference schemes is proved by the method of energy inequalities.

KW - Convergence

KW - Finite difference method

KW - Stability

KW - Time-fractional diffusion equation

UR - https://www.scopus.com/pages/publications/85129837022

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BT - Mathematics and its Applications in New Computer Systems - MANCS 2021

A2 - Tchernykh, Andrei

A2 - Alikhanov, Anatoly

A2 - Babenko, Mikhail

A2 - Samoylenko, Irina

PB - Springer Science and Business Media Deutschland GmbH

T2 - International Conference on Mathematics and its Applications in New Computer Systems, MANCS 2021

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Alikhanov A, Apekov A, Huang C. A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders. In Tchernykh A, Alikhanov A, Babenko M, Samoylenko I, editors, Mathematics and its Applications in New Computer Systems - MANCS 2021. Springer Science and Business Media Deutschland GmbH. 2022. p. 515-523. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-030-97020-8_47

A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this