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 -