Open AccessNew versions of the least-squares collocation method for solving differential and integral equations
Author(s) -
В. П. Шапеев,
Sergey Golushko,
Vasily Belyaev,
Luka Bryndin,
P. L. Kirillov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1715/1/012031
Subject(s) - collocation method , mathematics , orthogonal collocation , collocation (remote sensing) , integral equation , nonlinear system , least squares function approximation , differential equation , mathematical analysis , ordinary differential equation , computer science , physics , statistics , quantum mechanics , machine learning , estimator
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.