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New versions of the least-squares collocation method for solving differential and integral equations. / Shapeev, Vasily; Golushko, Sergey; Belyaev, Vasily et al.

In: Journal of Physics: Conference Series, Vol. 1715, No. 1, 012031, 04.01.2021.

Research output: Contribution to journal › Conference article › peer-review

Harvard

Shapeev, V, Golushko, S, Belyaev, V, Bryndin, L & Kirillov, P 2021, 'New versions of the least-squares collocation method for solving differential and integral equations', Journal of Physics: Conference Series, vol. 1715, no. 1, 012031. https://doi.org/10.1088/1742-6596/1715/1/012031

APA

Shapeev, V., Golushko, S., Belyaev, V., Bryndin, L., & Kirillov, P. (2021). New versions of the least-squares collocation method for solving differential and integral equations. Journal of Physics: Conference Series, 1715(1), [012031]. https://doi.org/10.1088/1742-6596/1715/1/012031

Vancouver

Shapeev V, Golushko S, Belyaev V, Bryndin L, Kirillov P. New versions of the least-squares collocation method for solving differential and integral equations. Journal of Physics: Conference Series. 2021 Jan 4;1715(1):012031. doi: 10.1088/1742-6596/1715/1/012031

Author

Shapeev, Vasily ; Golushko, Sergey ; Belyaev, Vasily et al. / New versions of the least-squares collocation method for solving differential and integral equations. In: Journal of Physics: Conference Series. 2021 ; Vol. 1715, No. 1.

BibTeX

@article{bc4edd2564cb4649961c7f3be1ac00eb,
title = "New versions of the least-squares collocation method for solving differential and integral equations",
abstract = "This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one- and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.",
author = "Vasily Shapeev and Sergey Golushko and Vasily Belyaev and Luka Bryndin and Pavel Kirillov",
note = "Funding Information: The research was partly carried out within the framework of the Program of Fundamental Scientific Research of the state academies of sciences in 2013-2020 (projects Nos. AAAA-A17-117030610136-3 and AAAA-A19-119051590004-5), was supported by the Russian Foundation for Basic Research (project no. 18-29-18029) and was carried out within the framework of the grant from the Russian Science Foundation (project no. 18-13-00392). Publisher Copyright: {\textcopyright} 2021 Institute of Physics Publishing. All rights reserved.; International Conference on Marchuk Scientific Readings 2020, MSR 2020 ; Conference date: 19-10-2020 Through 23-10-2020",
year = "2021",
month = jan,
day = "4",
doi = "10.1088/1742-6596/1715/1/012031",
language = "English",
volume = "1715",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - New versions of the least-squares collocation method for solving differential and integral equations

AU - Shapeev, Vasily

AU - Golushko, Sergey

AU - Belyaev, Vasily

AU - Bryndin, Luka

AU - Kirillov, Pavel

N1 - Funding Information: The research was partly carried out within the framework of the Program of Fundamental Scientific Research of the state academies of sciences in 2013-2020 (projects Nos. AAAA-A17-117030610136-3 and AAAA-A19-119051590004-5), was supported by the Russian Foundation for Basic Research (project no. 18-29-18029) and was carried out within the framework of the grant from the Russian Science Foundation (project no. 18-13-00392). Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved.

PY - 2021/1/4

Y1 - 2021/1/4

N2 - This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one- and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.

AB - This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one- and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.

UR - http://www.scopus.com/inward/record.url?scp=85100730730&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1715/1/012031

DO - 10.1088/1742-6596/1715/1/012031

M3 - Conference article

AN - SCOPUS:85100730730

VL - 1715

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012031

T2 - International Conference on Marchuk Scientific Readings 2020, MSR 2020

Y2 - 19 October 2020 through 23 October 2020

ER -

ID: 27875583