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

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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.

Original languageEnglish
Article number012031
JournalJournal of Physics: Conference Series
Volume1715
Issue number1
DOIs
Publication statusPublished - 4 Jan 2021
EventInternational Conference on Marchuk Scientific Readings 2020, MSR 2020 - Akademgorodok, Novosibirsk, Russian Federation
Duration: 19 Oct 202023 Oct 2020

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