A Note on Parabolic Difference Equations on Manifold

Allaberen Ashyralyev; Fatih Hezenci; Yasar Sozen

doi:10.1063/5.0115369

A Note on Parabolic Difference Equations on Manifold

Allaberen Ashyralyev
, Fatih Hezenci
, Yasar Sozen

Division of Topology

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

Abstract

In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given.

Original language	English
Title of host publication	5th International Conference of Mathematical Sciences, ICMS 2021
Editors	Huseyin Cakalli, Ljubisa D. R. Kocinac, Allaberen Ashyralyev, Robin Harte, Mehmet Dik, Ibrahim Canak, Hacer Sengul Kandemir, Mujgan Tez, Ozay Gurtug, Ekrem Savas, Nazlim Deniz Aral, Filiz Cagatay Ucgan, Onder Sahinaslan, Charyyar Ashyralyyev, Sefa Anil Sezer, Arap Duran Turkoglu, Oruc Raif Onvural, Hakan Sahin
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735442580
DOIs	https://doi.org/10.1063/5.0115369
Publication status	Published - 7 Nov 2022
Event	5th International Conference of Mathematical Sciences, ICMS 2021 - Istanbul, Turkey Duration: 23 Jun 2021 → 27 Jun 2021

Publication series

Name	AIP Conference Proceedings
Volume	2483
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	5th International Conference of Mathematical Sciences, ICMS 2021
Country/Territory	Turkey
City	Istanbul
Period	23/06/21 → 27/06/21

Keywords

Difference equations on manifolds
difference schemes
self-adjoint positive definite operator
well-posedness

Access to Document

10.1063/5.0115369

Cite this

Ashyralyev, A., Hezenci, F., & Sozen, Y. (2022). A Note on Parabolic Difference Equations on Manifold. In H. Cakalli, L. D. R. Kocinac, A. Ashyralyev, R. Harte, M. Dik, I. Canak, H. S. Kandemir, M. Tez, O. Gurtug, E. Savas, N. D. Aral, F. C. Ucgan, O. Sahinaslan, C. Ashyralyyev, S. A. Sezer, A. D. Turkoglu, O. R. Onvural, & H. Sahin (Eds.), 5th International Conference of Mathematical Sciences, ICMS 2021 Article 060003 (AIP Conference Proceedings; Vol. 2483). American Institute of Physics Inc.. https://doi.org/10.1063/5.0115369

Ashyralyev, Allaberen ; Hezenci, Fatih ; Sozen, Yasar. / A Note on Parabolic Difference Equations on Manifold. 5th International Conference of Mathematical Sciences, ICMS 2021. editor / Huseyin Cakalli ; Ljubisa D. R. Kocinac ; Allaberen Ashyralyev ; Robin Harte ; Mehmet Dik ; Ibrahim Canak ; Hacer Sengul Kandemir ; Mujgan Tez ; Ozay Gurtug ; Ekrem Savas ; Nazlim Deniz Aral ; Filiz Cagatay Ucgan ; Onder Sahinaslan ; Charyyar Ashyralyyev ; Sefa Anil Sezer ; Arap Duran Turkoglu ; Oruc Raif Onvural ; Hakan Sahin. American Institute of Physics Inc., 2022. (AIP Conference Proceedings).

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title = "A Note on Parabolic Difference Equations on Manifold",

abstract = "In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various H{\"o}lder norms for the solutions of such boundary value problems. Furthermore, numerical results are given.",

keywords = "Difference equations on manifolds, difference schemes, self-adjoint positive definite operator, well-posedness",

author = "Allaberen Ashyralyev and Fatih Hezenci and Yasar Sozen",

note = "Publisher Copyright: {\textcopyright} 2022 American Institute of Physics Inc.. All rights reserved.; 5th International Conference of Mathematical Sciences, ICMS 2021 ; Conference date: 23-06-2021 Through 27-06-2021",

year = "2022",

month = nov,

day = "7",

doi = "10.1063/5.0115369",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Huseyin Cakalli and Kocinac, \{Ljubisa D. R.\} and Allaberen Ashyralyev and Robin Harte and Mehmet Dik and Ibrahim Canak and Kandemir, \{Hacer Sengul\} and Mujgan Tez and Ozay Gurtug and Ekrem Savas and Aral, \{Nazlim Deniz\} and Ucgan, \{Filiz Cagatay\} and Onder Sahinaslan and Charyyar Ashyralyyev and Sezer, \{Sefa Anil\} and Turkoglu, \{Arap Duran\} and Onvural, \{Oruc Raif\} and Hakan Sahin",

booktitle = "5th International Conference of Mathematical Sciences, ICMS 2021",

}

Ashyralyev, A, Hezenci, F & Sozen, Y 2022, A Note on Parabolic Difference Equations on Manifold. in H Cakalli, LDR Kocinac, A Ashyralyev, R Harte, M Dik, I Canak, HS Kandemir, M Tez, O Gurtug, E Savas, ND Aral, FC Ucgan, O Sahinaslan, C Ashyralyyev, SA Sezer, AD Turkoglu, OR Onvural & H Sahin (eds), 5th International Conference of Mathematical Sciences, ICMS 2021., 060003, AIP Conference Proceedings, vol. 2483, American Institute of Physics Inc., 5th International Conference of Mathematical Sciences, ICMS 2021, Istanbul, Turkey, 23/06/21. https://doi.org/10.1063/5.0115369

A Note on Parabolic Difference Equations on Manifold. / Ashyralyev, Allaberen; Hezenci, Fatih; Sozen, Yasar.
5th International Conference of Mathematical Sciences, ICMS 2021. ed. / Huseyin Cakalli; Ljubisa D. R. Kocinac; Allaberen Ashyralyev; Robin Harte; Mehmet Dik; Ibrahim Canak; Hacer Sengul Kandemir; Mujgan Tez; Ozay Gurtug; Ekrem Savas; Nazlim Deniz Aral; Filiz Cagatay Ucgan; Onder Sahinaslan; Charyyar Ashyralyyev; Sefa Anil Sezer; Arap Duran Turkoglu; Oruc Raif Onvural; Hakan Sahin. American Institute of Physics Inc., 2022. 060003 (AIP Conference Proceedings; Vol. 2483).

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

TY - GEN

T1 - A Note on Parabolic Difference Equations on Manifold

AU - Ashyralyev, Allaberen

AU - Hezenci, Fatih

AU - Sozen, Yasar

PY - 2022/11/7

Y1 - 2022/11/7

N2 - In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given.

AB - In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given.

KW - Difference equations on manifolds

KW - difference schemes

KW - self-adjoint positive definite operator

KW - well-posedness

UR - https://www.scopus.com/pages/publications/85142525723

U2 - 10.1063/5.0115369

DO - 10.1063/5.0115369

M3 - Conference contribution

AN - SCOPUS:85142525723

T3 - AIP Conference Proceedings

BT - 5th International Conference of Mathematical Sciences, ICMS 2021

A2 - Cakalli, Huseyin

A2 - Kocinac, Ljubisa D. R.

A2 - Ashyralyev, Allaberen

A2 - Harte, Robin

A2 - Dik, Mehmet

A2 - Canak, Ibrahim

A2 - Kandemir, Hacer Sengul

A2 - Tez, Mujgan

A2 - Gurtug, Ozay

A2 - Savas, Ekrem

A2 - Aral, Nazlim Deniz

A2 - Ucgan, Filiz Cagatay

A2 - Sahinaslan, Onder

A2 - Ashyralyyev, Charyyar

A2 - Sezer, Sefa Anil

A2 - Turkoglu, Arap Duran

A2 - Onvural, Oruc Raif

A2 - Sahin, Hakan

PB - American Institute of Physics Inc.

T2 - 5th International Conference of Mathematical Sciences, ICMS 2021

Y2 - 23 June 2021 through 27 June 2021

ER -

Ashyralyev A, Hezenci F, Sozen Y. A Note on Parabolic Difference Equations on Manifold. In Cakalli H, Kocinac LDR, Ashyralyev A, Harte R, Dik M, Canak I, Kandemir HS, Tez M, Gurtug O, Savas E, Aral ND, Ucgan FC, Sahinaslan O, Ashyralyyev C, Sezer SA, Turkoglu AD, Onvural OR, Sahin H, editors, 5th International Conference of Mathematical Sciences, ICMS 2021. American Institute of Physics Inc. 2022. 060003. (AIP Conference Proceedings). doi: 10.1063/5.0115369

A Note on Parabolic Difference Equations on Manifold

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